SIL problems!

Let me first say I love my sil but oh my gosh, since her son was born in January she has been pissing me off! She's a FTM and a single one since the baby daddy didn't want anything to do with the pregnancy but now he wants to be part of his sons life and she doesn't want to let him. I've tried multiple times to convince her to let him because no matter what he is the dad and some guys have a harder time becoming a father than others. He'll even buy his son whatever he needs and will even buy her things but she's holding a grudge about him not being there for her through the pregnancy. So that's one thing, second is I watch my nephew mon-fri 7am-4pm and I don't have her pay me because I felt bad that she's doing it on her own but now I'm just annoyed. So my mil and sil never put him down! Even when he's sleeping they don't want to put him down and I understand that it's good with babies and it's her motherly instinct but now whenever you put him down he throws the biggest tantrums and screams bloody murder! I can't do anything because of the way he is now and what pisses me off more is that she notices he's that way now because of them and so she doesn't like to take her OWN SON out with her because of his tantrums! Last Saturday she asked me at 8am if I could watch him because she didn't want to take him with her to go run errands cause he cries when he's in his car seat or stroller, I told her no cause I had things to do myself and she basically blamed me for not being able to get anything done that day because she HAD to take her son with her. Like wtf! I'm not his personal nanny to be there all the damn time and he's your responsibility not mine! Third, she took last Friday off from work so she could take him to get his 2 month shots that have been delayed but she decided she didn't want to go anymore, so on Monday she asked me if I can take him to go get his shots cause she didn't want to take anymore time off work to take him and the office closes before she gets off work. I ended up taking him Wednesday after she called the dr and signed a medical note saying I can take him and I only took him cause I'd rather him not get sick. Well I told her that the dr said to only give him baby Tylenol if he gets a high fever, which he never did. He was fine, not in pain, no fever. He was just throwing his regular tantrums, so she decides to give him baby Tylenol in the morning and at night for two days straight. I told her what does she think she's doing and she tells me "he's being fussy so I think he's in pain so I'm giving him medicine." I told her to stop cause he doesn't need it! He's being his normal fussy self like always and is not in pain because I'll massage his thighs where he got his shots and he never cries or anything, he smiles when I do it. Yet I can't tell her anything because it's HER SON. Yep that's what she told me! Plus he's always super fussy like he's the most fussy baby I have ever met and I don't know why but I told her to go get him checked for stomach problems because they NEVER burp him and later in the day he'll start spitting up a lot because they don't burp him. He's almost three months and needs to be burped Yet they don't like to listen to me.