Jess, I am seeing a lot of F.O.G. in your post. (Fear,Obligation,Guilt ) That's extremely common in those of us who have been subjected to unhealthy family dynamics. My "foggy" brain kept me enmeshed in several unhealthy relationships with members of my family, my circle of friends and AXH . It was not easy for me to detach from those people that I loved very much, but it was neccesary to do so if I wanted to get myself healthy and then start living a healthier, happier life. I wanted to break the cycle, I wanted my children to see it didn't have to be "that way". Your daughter is young enough she wouldn't have to "unlearn" the unhealthy lessons if she doesn't get used to growing up in that dynamic like you and I (and my kids) did.
People who lead toxic lives will be toxic to be around as long as they choose to live that way, no matter how much we love them. It doesn't usually make them bad people, but just because someone isn't evil, doesn't mean we give them a pass for their unhealthy behavior, ESPECIALLY when it affects us and our children in negative ways. I think you are doing the right thing detaching from the people in your family who are not setting good examples of health and happiness for your daughter.
The fact you don't want to take your daughter to your sister's home for reasons of her physical safety sounds like a good enough reason for YOU to stay away too. Your instincts matter, please keep listening to them. Try to battle back that F.O.G.
I know you love your sister. Is it possible you could do something special for her and the new baby separate from this baby shower? A special luncheon or a picnic to a favorite childhood spot, complete with balloons, gifts, goodies etc ? I realize that a lot of baby showers are co-ed these days, but it seems kind of creepy to me that he wants to control the whole thing by his man-handing it. I realize I'm generalizing here, but most men wouldn't want anything to do with the generally very girly activity of planning a baby shower. I find that concerning. Some people even have more then one shower for various different reasons, though from what you have said of your sister's husband, she probably wouldn't be "allowed" to attend a different gathering.
Good luck Jess, I know just how hard it is getting untangled from family stuff. ( I moved 3K miles away and they still sometimes try to get me involved in the drama... nope!.. it's less foggy where I live now :P )
I hope you stick around for support while you sort these things out.
Hugs.