I'm going to tell my sister she shouldn't expect our mom to provide full-time babysitting
Why do you want to tell your sister that mom can't provide full-time babysitting?
I want to blow off some steam and spill my anger to her.
I get how you might be feeling. At the end of the day, your sister might need some help. Taking care of a baby is especially hard if you work very hard. Your mom might actually want to babysit because it's her grandchild. 
I won't tell my mom to quit but I am still going to complain about it.
It's your mom's right if she wants to keep babysitting or not, and I believe that it's better to just come clean about how you feel with her always trying to help out. Sometimes it pays to be independent, and your sister should learn how take care of the kids herself. However, would it be fair to say that this might all just be stemming from being jealousy?