I adopted my ginger tabby almost 5 years ago from the RSPCA as a kitten. He has been an indoor cat since day one. It is certainly a hard one isn't it! I too have struggled with worrying if I am being cruel by keeping him indoors and worrying if I am preventing him from engaging in natural behaviors.
I live in a particularly busy area and therefore the thought of him being hit by a car freaks me out!!!! I am lucky that Bodhi is not particularly interested in going outdoors as yours is. He will come out into our courtyard under supervision, sniff around and then head back indoors. There has been to odd occasion where a loud noise or something spooks him so then he does bolt and hide. Maybe this is what your cat is doing considering she was not raised with an understanding of the outdoors? Does she get along with your children?
Do you keep your cat active? This is crucial and can be easily neglected, especially now you have children. I find when i get busy with work and dont take the time to keep Bodhi mentally stimulated, there is a change in his behaviour. He gets pretty stroppy for a usually placid, loving cat.
Get some big lovely scratchy posts, balls to chase, toys to "hunt"...but as with kids, it's usually the more simple things that they love the most! For example, his favorite treat is a small branch brought in from outside....he'll spend ages having a good sniff, chew and then drags it around the house...his little taste of nature I suppose!
First and foremost, they need the attention above anything else since they are confined to the house. Maybe try to consciously give your cat playtime, as you used to e.g. as you explained with walks around the yard. Some old routine may calm her down. Don't forget that cats are a creature of habit and while addition of your daughter was a huge life changing experience for you....your cat has to adapt to that too.
Best of luck xxxxx