Beyond what everyone else is saying here, I am currently staying at home 4 days a week with a 3 month old child, and I also take a few online classes, so I think I am in an unique situation to offer some insight.
At this point, I think I could take care of another child on top of my own. But it's taken me a very long time to get here, and even one child is a lot of work. On top of that, my baby is unusually placid. If you do end up getting a fussier child (likely if you you have two babies to take care of), it will be more difficult.
Babies need constant attention. Even now, when my baby can be distracted with toys and music, you're spending all your time looking at them and talking to them and playing with them. Two babies is not twice is much work. It's much more than twice as much work. Feeding a baby can twenty minutes. What do you do if the other baby starts crying? What about constant diaper changes? What about one baby waking the other baby up when it goes to sleep?
Taking care of a child - my own child - is mentally exhausting. If you're already feeling a lot of stress before the baby even comes, I don't think you need any added stress.
I'm sure people have already told you this, but when you're taking care of a baby you get ZERO work done. None. I get all my work done during the weekend. I had a presentation on Saturday and stayed up most of the night to do it. I gave the presentation on one hour of sleep. If you have to take care of the house, take care of dogs, and do class work, I don't know if you should be taking on extra work.
All in all, I really feel for your SIL's situation. It's hard taking care of the baby with two parents. I can hand him off for a few hours, and vice versa. It's going to be VERY difficult for her. However, she's the one who put herself in that situation. I think it's much better to tell her no now, and - depending on how your baby is, and you feel when the time comes - you can help her out a little now and then. Babysitting once or twice a week is very different from the constant care she seems to be expecting from you. Saying no now and yes later is much better than saying yes now and no latter.
Most important, though, you should keep in mind that you are under zero obligation to help her out. It would be very nice of you to offer care, and there might be a sense of duty from a societal or filial perspective, but if she or her family get mad at you for not doing so, then they're being idiots. Take care of yourself and your family first.