I completely agree with Peaches and with JenJay. Your SIL just wants to be in control.
As do I. This sounds like SIL wants to control the event and might be using the baby's illness as an excuse. Honestly, if she were truly concerned about leaving the house, illness, etc, the last thing she should want to do is invite *anyone* over. Germs, possible coming-down-with-something even if someone feels okay, the door opening and introducing a draft...no, if I were a concerned mother, I would have backed out entirely with profuse apologies. That would have been 100% understandable.
The whole deal with "letting you host" was downright weird. I'd be pretty irked, too. If I were you and your DH, I'd either show up with a salad/dessert//bottle of soda (as in, token item) let her host and afterwards, keep this "filed for reference" for future events. (Did you say you had friends you planned to meet? Maybe you can host a gathering for them and a less formal get-together for family as well if you were looking forward to hosting?)
Assuming the SIL just wants to "control" the situation is cruel. I've been in a very similar situation to SIL, I had a newborn in ICU for 3 weeks before he was even allowed to come home. This isn't about control beyond the fact that BOTH of the parents (stop blaming SIL!) want to keep their new baby healthy and, you know, ALIVE. They wouldn't be having people over if the doctor hadn't OKd it. Trust me. Good grief, people. We're talking about a life here. It's a little more important than where dinner is held.
Yeah, a lot of these replies are really surprising to me. Whatever the SIL's past, this is a fragile new baby that was very ill. Not having to take the baby out in the elements alone is a reason to have the event at the SIL's house.
I realize the OP is frustrated but I really have a hard time believing that someone who's new baby was deathly ill is really going to spend time creating this devious plot to "control" a family holiday celebration. Even parents of a healthy new baby are often encouraged to keep the baby home initially during cold winter months. It is totally reasonable and makes sense that the OP's SIL wants to do the same.
It is no indication that the OP's house "isn't good enough" and I do actually think the SIL was trying to be considerate by saying since you had planned to host, that you could just continue your plans but at their house.
OP, is this also a SIL that previously lost a child, or am I thinking of someone else? If so, it makes even more sense that she is overprotective. I think in these cases we might realize people are extremely concerned for their baby's welfare and be a little sensitive to that. I really think writing off this situation as "using the baby as an excuse to control things" is pretty callous way of looking at it.