Dear STATA community,

This is my first post and I hope that you can help me with my problem.
In a nutshell, I run a regression to estimate the impact of workers' country of birth (reference: native workers) on wages. Besides, I also control for sex (female = 1) and education.

Code:
. reg log_sal_bonus i.Birth_region_gen_final_a sex i.education [aw=Pond_AB], r
(sum of wgt is 20,200,447.423307)

Linear regression                               Number of obs     =  1,304,858
                                                F(8, 1304849)     =   33434.19
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3156
                                                Root MSE          =     .30553

-----------------------------------------------------------------------------------------------------
                                    |               Robust
                      log_sal_bonus |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------------------+----------------------------------------------------------------
           Birth_region_gen_final_a |
               First - 2-Developed  |    .024678    .001561    15.81   0.000     .0216185    .0277375
 First - 3-Transition_&_Developing  |  -.0927497   .0012075   -76.81   0.000    -.0951164   -.0903829
                            Others  |   .0698681   .0051349    13.61   0.000      .059804    .0799323
              Second - 2-Developed  |  -.0150958   .0012651   -11.93   0.000    -.0175754   -.0126162
Second - 3-Transition_&_Developing  |  -.1198456   .0018575   -64.52   0.000    -.1234863   -.1162048
                                    |
                                sex |  -.1625361   .0007542  -215.51   0.000    -.1640143   -.1610579
                                    |
                          education |
                                 2  |   .0767518   .0007308   105.02   0.000     .0753195    .0781842
                                 3  |    .476564    .001068   446.23   0.000     .4744708    .4786572
                                    |
                              _cons |   2.816732   .0006466  4356.09   0.000     2.815464    2.817999
-----------------------------------------------------------------------------------------------------
Now, I want to run a regression with interactions between the country of birth and sex instead of splitting into two sub-samples (female and male). My output seems quite logical if we look at the females' coefficients (in fact, the females' coefficients here are almost the sum of the coefficients in my previous table + sex).

Code:
reg log_sal_bonus i.Birth_region_gender i.education [aw=Pond_AB], r
(sum of wgt is 20,200,447.423307)

Linear regression                               Number of obs     =  1,304,858
                                                F(13, 1304844)    =   20634.97
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3159
                                                Root MSE          =     .30546

---------------------------------------------------------------------------------------------------------
                                        |               Robust
                          log_sal_bonus |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------------------------+----------------------------------------------------------------
                    Birth_region_gender |
               Belgium - Natives women  |  -.1640748   .0008906  -184.22   0.000    -.1658204   -.1623292
                 First - Developed men  |   .0350259    .002058    17.02   0.000     .0309922    .0390595
               First - Developed women  |  -.1566719   .0022561   -69.44   0.000    -.1610938   -.1522501
                    First - Others men  |   .0756946   .0064093    11.81   0.000     .0631327    .0882566
                  First - Others women  |  -.1058152   .0085449   -12.38   0.000    -.1225629   -.0890675
   First - Transition_&_Developing men  |  -.1048025   .0014601   -71.78   0.000    -.1076643   -.1019407
 First - Transition_&_Developing women  |  -.2272819   .0020083  -113.17   0.000    -.2312182   -.2233457
                Second - Developed men  |  -.0141235   .0015387    -9.18   0.000    -.0171394   -.0111077
              Second - Developed women  |  -.1813582   .0021551   -84.15   0.000    -.1855821   -.1771343
  Second - Transition_&_Developing men  |  -.1293338    .002309   -56.01   0.000    -.1338593   -.1248083
Second - Transition_&_Developing women  |  -.2649113   .0030794   -86.03   0.000    -.2709469   -.2588758
                                        |
                              education |
                                     2  |   .0768369   .0007309   105.12   0.000     .0754043    .0782695
                                     3  |   .4765397   .0010672   446.51   0.000      .474448    .4786315
                                        |
                                  _cons |   2.817192    .000665  4236.48   0.000     2.815889    2.818495
---------------------------------------------------------------------------------------------------------
However, I am worried of the fact that I may also have to include interactions between education and sex since I also run the interaction of country of birth and sex and the impact of education may be different for men and women. I do that and unfortunately, my output is quite different. The females's coefficients are extremely positive compared to native men and from a labour economic point of view, that is not possible.

Code:
. reg log_sal_bonus i.Birth_region_gender i.education#i.sex [aw=Pond_AB], r
(sum of wgt is 20,200,447.423307)
note: 3.education#1.sex omitted because of collinearity

Linear regression                               Number of obs     =  1,304,858
                                                F(15, 1304842)    =   18325.00
                                                Prob > F          =     0.0000
                                                R-squared         =     0.3172
                                                Root MSE          =     .30518

---------------------------------------------------------------------------------------------------------
                                        |               Robust
                          log_sal_bonus |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------------------------+----------------------------------------------------------------
                    Birth_region_gender |
               Belgium - Natives women  |   .2846285    .001693   168.13   0.000     .2813103    .2879466
                 First - Developed men  |   .0345303   .0020482    16.86   0.000     .0305158    .0385448
               First - Developed women  |   .2924861   .0027622   105.89   0.000     .2870724    .2978999
                    First - Others men  |   .0730843   .0063722    11.47   0.000     .0605951    .0855736
                  First - Others women  |   .3455405   .0086388    40.00   0.000     .3286088    .3624722
   First - Transition_&_Developing men  |  -.1030127    .001467   -70.22   0.000    -.1058881   -.1001374
 First - Transition_&_Developing women  |   .2184794   .0026264    83.19   0.000     .2133318     .223627
                Second - Developed men  |   -.013088   .0015412    -8.49   0.000    -.0161087   -.0100673
              Second - Developed women  |    .265587   .0026116   101.70   0.000     .2604684    .2707056
  Second - Transition_&_Developing men  |  -.1282039   .0023131   -55.42   0.000    -.1327376   -.1236702
Second - Transition_&_Developing women  |   .1830853   .0033804    54.16   0.000     .1764599    .1897108
                                        |
                          education#sex |
                                   1 1  |  -.4461616   .0017727  -251.68   0.000    -.4496361   -.4426872
                                   2 0  |   .0692601   .0008954    77.35   0.000     .0675052    .0710149
                                   2 1  |  -.3534031   .0017207  -205.38   0.000    -.3567757   -.3500306
                                   3 0  |   .4926451   .0013284   370.86   0.000     .4900414    .4952487
                                   3 1  |          0  (omitted)
                                        |
                                  _cons |   2.816362   .0007338  3838.17   0.000     2.814924      2.8178
---------------------------------------------------------------------------------------------------------
Can you tell me if I finally have to include interactions between the control variables (e.g. education) and sex? In that case, why do the coefficients become positive for women?
Or is it if enough to exclusively include control variables as in table 2?

Thank you so much for your help!