Ok, well I think Lilcamper & I have different viewpoints on this.
As far as I'm concerned, ensuring your dog is able to carry out a reliable Sit/Stay is extremely important. There are so many situations where it's useful & you just never know, it could even save the dogs life if it were in a situation where moving wouldn't be a good idea.
"Leave" is another very important thing to teach your dog, again it could save its life.
So, yes, in my opinion, if the dog isn't "on board" with staying or leaving when its told, it would be firmly corrected. One firm correction is way more beneficial than a 100 ineffective corrections as far as I'm concerned. But this is your dog, your baby, your hubby & it's up to you decide which method suits all of you.
You would be correcting the dog for not doing as you ask - sit/staying - so I don't see how she would relate this to the baby. I'm assuming that the dog understands sit/stay - if she doesn't, you'll have to teach her from scratch, without the baby, as you'll need to focus your full attention on the dog. Call her to her bed(I say "Bed" when I do this, so later on I simply say "Bed" & they know to go there), tell her sit/down(whichever you want), then Stay (I usually reinforce this with a hand signal), then treat & release (I use ok). Gradually increase the time that she stays on the bed. Lots of short sessions with positive reinforcements ending on a good note is much better than one long session that ends badly. It's important that you watch her very closely, & as soon as she attempts to break the "Stay", you correct her with a very firm "no" & repeat "Stay".
Once she's able to carry out a good sit/stay (or if she is already), then you can start doing it with your baby around. To start with you're probably going to need another person to help you. Depending on how excited she gets, it might be a good idea to put a soft lead on her. So you send her to bed with a "stay", have your hubby standing near ready to correct her the very second she starts to move - then pick up your baby. It's important that your hubby corrects her before she breaks her stay, with a quick pull on the lead, saying no & stay quite sharply. If she stays & is quiet, she's given a high value treat (bits of chicken/hot dog/cheese)
I would practice this with your hubby next to the dog & you holding the baby to start with, if she gets more upset when he's holding the baby as that'll be easier. Then swop positions letting hubby hold the baby once she understands what you want from her. When you're by yourself during the day, providing she's a lead on, you can simply put your foot on the lead telling her "no" if she starts to break the "stay". Also by using the lead to correct her, she's less likely to become hand shy, which can happen if you're constantly grabbing her by her collar - it's important that she associates your hands as something that delivers good things - food/cuddles/toys - not bad things.
I wonder if you're only paying attention to the dog when the baby is asleep? This needs to change - good things like feeding time/walks/playing etc happen when the baby is around - when baby isn't around try to ignore the dog as much as possible.
You could try teaching her "Quiet" - so when she starts barking, tell her "Quiet" - if you do this quite sharply to start with, it'll should startle her into shutting up(lol), then immediately give her a treat - again you'll have to start slowly & build up the time.
Hope it's all not too garbled for you!