My mother is giving me the silent treatment, and didn't even call to wish me a happy birthday. But she still wants to see my two-year-old daughter for overnights. She asked to pick up my child at daycare and then drop her off at daycare the next day, so she wouldn't have to see me. I don't want to use my daughter as a weapon in our disagreement, but on the other hand, it seems that there are natural consequences of refusing to speak to me. What should I do?

Tell her that since there SEEMS to be a lack of communication you do not feel comfortable just dropping off your daughter. Put it back on her in a way that she doesn't even realize it was put back on her by using I feel and I am not so sure and I need to feel comfortable type statements so she doesn't feel 'offended by you attacking her'. Which is the way people that give the silent treatment do do.
Then it is on her to make the next move to decide to talk to you or not have her dropped off

What should you do ? Well patch things up of course, please don't make bad blood between your mom and you. You didn't say why she was giving you the silent treatment so it must have been a disagreement between you two. Mom's are irresplacable bri79. Don't make situations you will regret later on and good luck patching this up.