Delete the "to other loads", those aren't required and just muddy the situation. Make the #6 conductor a #8 75C conductor, so its ampacity matches the 50A I specified. The #8 can originate from the 125A OCPD if you like. Add the 100A secondary OCPD. And specify that the #8 is 10', and the #3 from the transformer to the secondary OCPD is 10' long. Then yes.
Also, your computation in the "1/3 of feeder size" box is wrong. 25' tap rules are based on the ampacity--the ampacity of the of the tap conductor has to be at least 1/3 of the OCPD providing SC/GF protection. Or for motor conductors under 430.28, 1/3 the ampacity of the feeder conductor being tapped (since the OCPD maybe greater than that conductor's ampacity).
Cheers, Wayne
