Advice please

I'm a young single mother so I had to go back to work and leave my 6 month old in the care of my mother. Lately my mother has been joking around a lot that I'm the step mother or nanny because I'm kind of strict with daughter. She tells my daughter she's her mother and it really bothers me. I spoke to her about it and she gets mad and tells my siblings I made her feel bad etc.

I live with her so when I am off work and am at home spending time with my daughter (laying with her or in the living room watching her run in her walker) she comes and tries to take her from me or sends my younger siblings to take my daughter to her. When I tell her no she makes up things and tells my family I was rude and told her not to touch and have contact with my daughter. If I had somebody else to leave my daughter with I would but I don't. I don't trust day cares...

Can somebody give me advice? Should I resort to a daycare or what should I do? I'm really tired of this. She doesn't understand she's just the grandmother, not the mother.