And many parents we know (ourselves included) give up exercise. If at all possible, try to maintain some semblance of an exercise routine.
For people who aren't are so fortunate, I always recommend that they look into Kettlebell Simple & Sinister on Amazon from Pavel Tsatsouline (there's a new version, recently released, easy to read and very dense with information and incredible strength training insights).
Simple & Sinister is essentially a 20 minute, no nonsense, 100% legitimate strength training routine that can be done daily, even in combination with other training programs and workouts. Kettlebells take up essentially no space and if you buy a reputable brand you will have this strength training implement for the rest of your life.
For what it's worth, that means that you're actually at an easier phase than you will be when the kids get older. Infants are time-consuming in many ways, but they also sleep a lot and have few external needs of their own.
When your kids stopping napping and start acquiring their own friends and activities, the time commitment goes up a lot, especially when they are still too young to do much for themselves.
Elementary age sort of plateaus: the amount of activities goes up, but they can take care of more of their own maintainance too. I don't know what middle school is like yet, but my hunch is that the time commitment starts going down when they become old enough to go to activities on their own.
Kettlebells, traditionally, jump in 4kg increments. So, on average, with this program, you start with a single 16kg kettlebell, and then move to a 20kg, on up to 32kg.
I have a lot of kettlebells... 2x12kg, 2x16kg, 2x20kg, 1x24kg, 1x28kg, 1x32kg, 1x36kg, 1x40kg. They have a small footprint. I leave them all in a corner in the garage and they take up very little space, maybe 3 square feet. I'm on a different (non-kettlebell) program right now. But, I am using the 32kg on days that are not my main training days for strength-endurance purposes (I like doing between 300 and 500 heavy swings a week).
Sorry for the brevity, but I wanted to respond. Hope it helps.