I'm sure that is hard. FWIW, I take DS to the same daycare everyday (since April) and somedays he's just content to start playing with the toys. Somedays he starts crying and trying to crawl back inside the womb. I hate watching him cry on those bad days. But I do know that he settles down shortly after I leave.
I think it's very nice that you are allowing your MIL sometime with your DD as well. And presumably you are comfortable with your MIL's ability to babysit and nurture your DD. I guess my point is that you know you are leaving her in good hands, so try to focus on the fact that she's reacting like any baby/toddler would, and you, as the adult, are the one making the decisions. In reality, you are not harming her. And in general in her life, obviously there will be many times that she doesn't want to do something, and she has to do it.