need advice

Zainab • 2 early MC, 1 baby and another BFP hope this is my second rainbow baby
So today my mom took my little one out to the store with her and I found out when i came home and i'm ok with it but my husband was furious how she didnt take "permission" from me or him (BTW my mom babysits while i'm at work and we have a nanny at home to help with house work) and he went on a rant how I wouldnt be ok with his mom picking up my daughter without me knowing and next time that if my mom wants to go out to not take my daughter unless i'm with her and leave the baby with the nanny.
I told my mom this and she is very upset that all she wanted to do was entertain my little one who was extra cranky and going out calms her down.  
A littl background:
I had a fight with my husband once about his mom feeding my daughter and giving her water when she was 3 months old even though she knows I don't allow it and did it anyway. Ever since then it's been like an eye for an eye. Whatever my parents do my husband gets angry. So tomorrow morning his mom is coming to pick my daughter up for the morning because my mom took her out in the morning and they "only see her once a week and when they see her she is cranky so they should get to see her in the mornings too" i told him fine as long as she is back when i'm back from work and they are taught how to warm breast milk. 
The thing is my mom is furious and crying about how he is treating her eye for eye and now she feels she has to "tip toe" around him and his mom is always talking to him and turning him against me and causing problems. And it shouldnt be this way. 
I really don't know what to do. I know she feels hurt and disrespected. She feels that he is ungrateful because we live with my parents in an apartment above the house we don't pay rent and she treats him like her son. And she insists that it's his mom talking to him and riling him up like this because it's so unlike him.
What the heck am I supposed to do? She wants to speak to him but I know that is going to be disasterous