I really liked doing Angelus at noon with the children.
I was babysitting my grandsons this weekend and I was really noticing the effect on the time I spent praying. It is way harder to fit in with little ones and you are doing well to manage as much as you have. Doing the duties of your state of life is also holy.
We say before meal prayers and night time prayers.
As far as other formal prayers, I have a hard time with them because I am so tired. So I have come up with an alternative. As I go about my day doing things like dishes, cooking, cleaning, etc, I pretend that I am doing this for the Holy Family. As I do things for my kids, especially when they drive me insane, I try to pretend I am taking care of a little baby Jesus. I play Catholic kid's songs during the day and sing them, as well as songs to the BVM. We talk about heaven and hell. Whenever any of them lies or steals we (myself and the perpetrator) kneel in front of a crucifix and say we're sorry and ask for help to do better next time.
In a few years I am sure I will be able to add more formal prayers.
These are both great responses!
I've heard it suggested at least 15 minutes a day depending on your state in life. Though often I struggle to put in any more than prayers before meals, night prayers with my little one and and our father with my husband. But it does make my whole day better if I can remember to pray the morning offering.
I often pray a gloria before starting a task, and some days I run over to the wall where we have 2 icons and a crucifix, and say "help!"

And my husband and I have been working on saying the rosary as a family on Friday nights (though sometimes we forget or are completely exhausted by the end of the week).
When my daughter was 3 months old she had a temporary case of reflux, so for a few weeks I had to sit and hold her upright for half an hour after every night feeding. My prayer life had been totally disrupted up until that point (which I'm sure is normal though not ideal), but I used it as an opportunity to start praying the rosary again. Maybe when this next baby is born I'll try to pray compline while I'm on "night shift".