I'd like to say I have the magic formula for juggling spending time with the family and organizing/cleaning/miscellaneous household chores versus writing time. I don't. It's not as simple as: for every hour spent with the family should be an hour writing. Or: 25% of your "free time" should be spent on your craft.
Your situation may vary from mine, and even then each day or week or month seems to be different.
Take this past weekend for myself, for example. I'm nearing the end of editing my novelette Guest of Honor which I thought I'd finish Friday night. Didn't happen. Okay, I got more done Saturday morning, so Saturday I'll finish it. Nope. I did get more written, but it was after the kids went to bed. Ask me how much writing I did Sunday--the Lord's day of rest, mind you. Go ahead ask me.
Very little, until the kids were in bed. Why? Too much other household chores to do, which seems to always get in the way.
Then, to top it all off, I have a laptop computer that's so darn old I'm beginning to wonder if my youngest was born after we got it (she's in 1st grade; my daughter, not the computer). The reason I bring this last one up is because there are times when the computer tries to do more than one thing it'll lock up for the next 15-30 minutes. Not fun.
Every artist/writer experiences struggles in their life. What are you doing to cope?
What do I do? I write. Whenever I get a chance. Some days may be an hour here and an hour there, others I may have 3-4 hours of uninterrupted time.
The key is where your priority lies.
(Final note: I finished editing Guest of Honor this morning)