Laine-
Your life sounds so much like mine, that it kind of spooked me a little!
I have a 2 1/2 year old and a 2 week old. Both boys though. I was over weight too, before kids, but with weight watchers and a lot of regular exercise, I lost and maintained a healthy weight( ok well, give or take a few pounds).
When I got pregnant with my older son, I gained like 60 lbs but lost most of it. I only had one baby to work around. But this time around is completely different.
Now with two I have no time. No time to exercise and no time to cook time consuming meals. My 2 week old cries when ever he's not being held. I'm BFing too (actually I'm typing with one hand right now!

) So I spend most of the day holding him. And my 2 1/2 year old is also more than a hand full. He's actually been diagnosed with ASD, and he has severe behavior problems. He has never sat calmly in a stroller. He screams to get out and throws fits. The classic exercise of putting the kids in a stroller and going for a walk is not an option for me.
My husband just graduated from grad school too. I know what its like not having your husband around, even though its for a good reason.
I wish I had suggestions for you. But I'm in the same boat. I wanted to let you know that you are not alone! I'm on here typing with one hand whenever I nurse the baby.
I'll tell you one idea that I'm kicking around. When I was inbetween my sophmore and junior year of highschool (over 10 years ago! Where does the time go??) I switched schools and did not want to start the new one being the weight I was. But I couldn't afford to go to a gym and I was too embarrassed to run out side...so in my very tiny bedroom (we lived in a tiny apartment sized beach house) I jogged in circles. Well they were more like ovals) Everyday I jogged in my room, for a set amount of time. Then did sit ups and leg lifts and other exercises that I could do in my room. Since then I've gotten spoiled with gym memberships. But I'm thinking about just walking in my livingroom. There I can hold my baby, stop whenever I need to to feed him if he starts crying; I don't have to worry about the weather outside or driving anywhere. Also I can break it up into say 3 groups of 10 minutes which would fit my day better then a 30 minute workout. So I guess that's one suggestion I do have, but I don't if it'll work with two kids!
Message me anytime you want to talk.