I just graduated and am a mom of young kids as well, so I know very well your struggle. Here are some tips I can offer that you hopefully will find helpful:

Get a sound machine/run a fan between you and the noise. It is hard to concentrate when you hear chaos.

YouTube videos are a great tool. I used tons of videos from Osmosis and Registered Nurse RN. I would sometimes try to multitask walking for exercise while listening to videos. Got 10 minutes before an appointment or while waiting for someone? Watch a video. Child actually playing quietly on their own for a bit? Watch a video. It makes the readings go faster when you already have a good grasp of the material.

Try to maximize studying time when it won't effect your family time. Can you wake up an hour earlier? Make arrangements with another mom to switch babysitting so you can study while your husband is at work? I don't know the details of your situation, but try to think about ways you can get study time in that will limit the amount of time you have to skip out on important family time.

Another thing is, you will soon figure out how much time you need to study to succeed. In the beginning, it's better to over study, but if you are getting very high scores on everything, it might be time to evaluate where you are splitting your time.

It will most likely be a struggle the whole way through your program, but it is worth it in the end!