Walking is the best starting point for any excersie programm, find reasons to walk more with the kids. After that yes lift the kids, and play, and you can start a very short bodyweight programme maybe once a week to start with.
My OH had various health issues that meant even walking 10 mins was painful, so we started off with 5 mins a day (after adjusing her gaite so it wouldn't cause pain) now she can walk 4 miles fine. I also gave her a very basic bodyweight program, 10 wall push-ups, 15 squats, 10 2 leg assist pull ups and 15 lying knee raises just one round at first, takrs less than 10 mins with the warm up, and she says she feels stronger for it.
Bottom line, it dosn't have to be hard or take a long time to do you good.
You know all those pictures of Adam and Eve where they have belly button? Think about it..................... take as long as you need........................