M.K.
Kudos to you for giving your children such wonderful healthy sleep experience! It's so great that your daughter is sleeping 11-13 hours a night!! And, despite what some of our own Moms may have thought years ago, a 21 month old also needs a daytime nap, in addition to those 11-13 hours of night sleep. (And, clearly, you can see this from the difficulty your daughter has in the late afternoon.)
I wish I had some great advice to give you. All I can offer you is this: you are probably right and should not go into her room -- she is likely expecting you (and you are SO much more interesting to her than relaxing in the crib!!) Unless your daughter is irritated by a poopy diaper and calling for you to change it, I don't think I would bother. But slather her bottom with Triple Paste before the nap to avoid diaper rashes.
Your schedule is really hectic and you are doing the best you can. Unfortunately, your daughter may not be ready for nap at 12pm. I know you want her to get at least 2 hours...but do you think she would end up getting more sleep if you delayed the nap until 12:30 or 12:45 and put her in the car as the last thing you do before you leave? It may not be 2 hours, but maybe she'll go to sleep right away. Even 1 1/2 hour nap would be better than no sleep at all.
Best of luck and keep up the wonderful healthy sleep habits!!