Daughter does not call me mom/mommy?

A lot of kids go through the stage of calling their parents by their first name. If the child knows it bothers you, and you make a big deal out of it, she is most likely to continue. Try not responding to her when she calls you by your first name. If she wants something, explain to her she has to call you mom. It will be a fight at first toddlers can be pretty stubborn, but in the long run it will work out. You also do need to set the boundaries with your own mother. Explain that your daughter is yours, and you don't appreciate it. If she keeps feeding into your daughter calling her mom, I would look into other childcare options, because she is not respecting your wishes. Tell your mom you don't want to fight with her, but this is something that is really stressing you out.