Sil rant

Before I start this rant, let me tell you, my sil is very self centered and my mil isn't helping. If everything isn't about my sil, one if not both of them, will make sure it becomes about her. My sil is mad bc she feels like she doesn't get to hold the baby enough...if she's at our house and she's not holding her she's mad, if we're at church, she has to b the one holding her, anywhere we are she has to have her...she even tried to take her away from family visiting from out of state that won't get to see her very often and got mad bc they said no. Anyways, she was mad the other day bc they came over for dinner after my daughters first night of daycare and my first day back to work. I was sitting at the table before dinner and she asked to hold her and I said no bc I hadn't seen her all day and I wanted to hold her. I didn't say it mean either. She was so mad she didn't talk to me for the rest of the night and went and told my husband that she had asked several times to hold her and just wasnt letting her hold her. So my husband came and took her from me and gave her to my sil.😠 that night he told me wat she said and I told him my side and he believed me. A couple days later, I get told that my husband and sil got into it bc she said something about me not letting her hold her, same situation brought up again. He defended me at that moment but when we talked he told me that we were going to hav a date night so my sil could watch her...#1 we don't hav the money to go out, and #2 that's not how "babysitting" works. I told him that and he got defensive and blamed me for 'not wanting to have a date night'. So now, if we're anywhere with her, she has to hav her. Bc if I tell her no, then I'm being 'overprotective'. I am her mother, so if i wanted to be 'overprotective', I have every right. It's not like I don't let her hold her so idk what her deal is. I hav a friend that just had a baby as well. Whenever my sil goes over there, my sil stays for hours bc my friend needs to do things around the house and let's her take care of him. I was not one of those mom's that wanted or needed any help, with the baby or housework, from anyone other then my husband. So my sil comes over expecting the same thing at our house and that doesn't happen and so she gets mad. Then comes my mil. She is also the kind of person that needs everything about her or her daughter. If it's not, she goes as far as crying. Over split milk I might add. She was on my sil side during the argument but wouldn't put her 2 sense in, suprisingly. She didn't make eye contact with me the next morning and wouldn't start a conversation either...I hav no idea what to do. My husband won't say anything to them bc that's is his family, and if they are upset about anything or have an opinion, then im wrong. So in this case, even though he knows i haven't done anything wrong, since his family thinks i am, then i am. I'm also not a person that like's confrontation and will start crying if I get confronted about anything..completely opposite from my husband. But if I say anything else to my husband, he gets super defensive bc I'm talking 'bad' about his family. I hav no idea what to do...someone please help!