I really understand you! I'm a stay-at-home mom as well. When I had my first I barely gained weight. But I got pregnant again when she was only 7 month old. I gained about 30lb with my 2nd pregnancy. When my 2nd daughter was born I was so busy. Forget exercises, I didn't even have time to brush my teeth.
My girls are 24 months and 9 months and it's gotten a little easier although far from perfect. My house is not as clean as I want it to be, I want to try a gazillion new recipes but end up cooking what's healthier and faster. I also started losing myself in never ending cycle of things that need to be done.
You know what helped me? I realized that there are only 24 hours in a day and in order to add a new activity in a day(exercise) something has to go. So I reviewed my day. Yes, it is still not perfect but I try to do something every day even if it's just 10 minutes. It makes me feel better. I would turn on the music and do jumping jacks for 4-5 songs. Or just dance. My kids love when mama is going crazy and giggle a lot. Can your kids join you? Make it a game, make it fun.
As you start doing something small but be consistent about it, it will become clear to you how to modify things. I'm even considering doing Chalean Extreme workout program. Just 2 month ago I would think it's impossible because my kids are so little.
We can be fitness buddies if you'd like:)
Never give up on a dream just because of the time it will take to accomplish it. The time will pass anyway.