Parenting disagreements

I have a 3 year old an almost 2 year old and a 5week old baby.. My mom watches my children while I go to work but she always has to try to put her sense into everything with the way discipline. It's extremely frustrating! This morning my daughter asked for eggs.. My sister cooked them for her and my daughter decided she didn't want to eat them.. Mind you she had nothing to eat today. I told my daughter she has to eat her eggs before we do anything else today and my mom starts offering her are all kinds of stuff.. Muffins, yogurt, cheese, etc... I said no she needs to eat her eggs! My mom then says anything she can eat is good and you and your sisters came out just fine and I said no what I cook for her she needs to eat and I am parenting how my husband and I want too... This is not the only problem I have ran into every time I yell at my children my mom always picks them up and makes everything seem like it's okay even if one has bitten the other... Anyone else have this problem? How would you handle my situation? I vacant afford putting them in daycare right now until I start receiving my income again and catch up on bills that we have missed from me being out with the new baby.