He is an amazing boyfriend and dad
Seriously? You are deluded, he is neither. He is a complete prick.
Ideally you need to leave but since you are deluded that won't happen so you need to stand up for yourself to ALL of them, they won't like it because currently they are all happy playing "Let's treat babygirlmama1 like shit and nobody say a word" game, you need to stop playing it with them and letting it happen!!
So tonight say "I'm skipping face time tonight and having a bath, I'll feed baby first"
If he objects say "I speak to them ever day, I am taking a break tonight, do not push me on this because I am sick of their treatment of me and yours too. I am standing up for myself from now on, they are your parents not mine, I don't need to speak to them daily, weekly is more than enough". Then start popping in and out of calls/leaving/just not participating.
Then with the in law's you need start saying " Fuck off". A sharp rightly timed fuck off will feel great, I did it myself once, it was great, was there a fall out? Yup but that meant not seeing them which was great too, all is fine now and it only needed doing once but mine are nowhere near as bad as yours. They are used to treating you like shit, you are allowing it, your oh is allowing it but just because he is allowing it does not mean you put up and shut up, you stand up for yourself!
"Don't drop the baby"
Thanks for the top tip Mary but I think I can manage
"Stop feeding so I can see my granddaughter"
Eh no, I am feeding her, in fact I'm going to take her upstairs and do it privately, see you during the week" then leave the room
"Come back my parents want to see the baby"
Frank they see her daily, they saw her now, she needs feeding, I am leaving. And leave the room.
Stop giving a fuck what these assholes think of you