It is pretty hard, isn't it? I have 3 little ones at home, and very little in the way of school/childcare (my choice, not complaining, just that I know its hard to find time!)
Here is what has worked for me:
1. Leaving the viola out so I can practice in dribs and drabs. My teacher actually says this is a good way to practice and on a good day I can get maybe an hour in this way.
2. A few times a week, dp takes the kids (no problems with this, just that he works quite long hours) and I do an hour of intense practice.
I have a rough practice schedule where I break stuff into 5-10 minutes vs sustained practice.
3. Just getting on with it as often as possible. Also, explaining that it doesn't work for me to be interupted. This has worked over a period of time, and it might help also that the oldest (5) recently started violin lessons himself, so he has an inkling of what is involved. (I am currently doing one of those Kreutzer studies with 40000 variations-he is doing similar with Suzuki and the Twinkle variations)
4. This might depend on the age of the kids, but for me it works to play some tunes they can dance to, to play them some of their favourites, etc.
If I didn't practice round my kids, I couldn't practice. I don't have the option of practising after they are in bed, even with a mute, as the house is too small. I do think a lot of this is perseverance, they get the message after a while that this is just what is DONE, and soon it becomes as normal and boring as washing up. (though I say that with the caveat that mine are 5, 4 and 1 so perhaps it is easier)
Just to add, some weeks I go to my lesson feeling I have hardly scratched the surface of what I could have done. This I find VERY frustrating!
I try to remember that, by just hanging in there, doing what I can, I am still getting better and better. Even practising just 20 minutes a day

will make me better than if I'd left the viola in its case.
Oh another tip, in weeks when I know I am going to struggle I talk to my teacher in advance and get him to help me prioritise. Another tip might be to ask if there are any exercises, theory work, etc that can be done away from the instrument.