I'm using mixed in Stata 15.1 to analyze a change in my variables at two time points. The data were generated in a randomized controlled medical study.

I am using these commands:
Code:
mixed small i.trt##i.time || id:, vce(robust)
margins, dydx(trt)
Although I'm paying close attention to the magnitude of the average marginal effect and the confidence intervals generated, I'm required to report p-values. In previous posts, Stata forum guides have suggested that if the p-values found 1) on the interaction term are quite different than 2) those generated by the margins, dydx command, some additional thought is required about what may be going on in the data.

My understanding is margins, dydx(var) generates a partial derivative with respect to var, measuring change in one variable while the others are held at their observed values.

Question1: Previous posts warned against relying on p-values from average adjusted predictions generated by margins. Is this also true of average marginal effects?
Question2: Could you please help me understand why certain variables (like "small" and "large" in my sample data) are significant by p-value on the interaction term (full derivative) but not in the margins command (partial derivative)? What can I learn about my data from these results?

A sample of my data is included below. Thank you in advance for your help and patience with my questions.

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input int id byte trt float(time small large)
1001 1 0 103.62028  2057.409
1001 1 2  83.89479  1673.689
1002 2 0  53.92493 1494.9586
1002 2 2  47.69698  1342.497
1003 1 0  95.35509 1537.0225
1003 1 2 74.401726 1095.4296
1004 2 0  61.61027 1367.5326
1004 2 2  49.44355 1145.2207
1005 2 0  94.76392  2612.909
1005 2 2  51.50049 1128.3427
1006 1 0  86.49782  1456.245
1006 1 2  65.66128 1411.7137
1007 2 0 121.33897 2947.7104
1007 2 2  101.6294  2035.673
1008 1 0  91.95323 1224.9602
1008 1 2  79.91485  1342.048
1010 2 0  78.80621 2073.3826
1010 2 2  62.52343   1607.94
1012 1 0  84.50602  1766.792
1012 1 2   86.0701  1849.264
1013 1 0  62.16099 1512.2836
1013 1 2  97.44263  1719.307
1015 2 0  83.27814 1706.0673
1015 2 2  60.52657  933.7055
1016 2 0 64.726036 1280.3625
1016 2 2  40.03102  733.2215
1017 2 0 104.22501 1412.9833
1017 2 2   81.8728 1217.6375
1018 2 0    81.716 1719.5686
1018 2 2 68.464676  1478.304
1020 2 0  143.5548 2186.3103
1020 2 2 140.04892  1548.019
1021 1 0 107.65491 2073.9907
1021 1 2         .         .
1022 1 0  76.36583  1707.781
1022 1 2  65.04529  1766.207
1023 2 0  57.13372  996.4772
1023 2 2  52.33152  905.7919
1024 1 0  61.39893   1060.22
1024 1 2  56.26431  802.0148
1025 1 0  127.1972   2630.19
1025 1 2         .         .
1026 2 0  79.88757 1726.9504
1026 2 2  54.34812 1155.5836
1027 1 0  60.56401  1684.059
1027 1 2  85.44836 2059.1775
1028 2 0  78.68946  1698.101
1028 2 2 66.658676 1222.4415
1029 2 0  97.76624  1751.821
1029 2 2  98.43185 1980.2466
end
label values trt diet_lab
label def diet_lab 1 "Treat1", modify
label def diet_lab 2 "Treat2", modify
label values time visitlab
label def visitlab 0 "Baseline", modify
label def visitlab 2 "6 Mos", modify
label var id "ID"
label var trt "Treatment"
label var time "Time"
label var small "Small"
label var large "Large"