Children
I have a 10 year old. I was diagnosed 6 years ago. The main thing is to keep experimenting with medications (dosage especially...e.g.I only need very low doses at the moment), under medical supervision of course. Be prepared to change medications, but give them a fair go. Give your GP & doctors a fair go, but be prepared to get support to change them if your relationship isn't working out.
I changed GP because my old GP was ok, but not very interested or knowledgeable about Bi-Polar. They can't be good at everything and sometimes you can change GP within a practice. The one good thing about Bi-Polar is that it can give you the courage to be honest...I said to my old GP that I liked her, but felt our partnership wasn't working and could she help me find someone with a specific interest in mental health...she did and now I've been with my current GP for 5 years!
I found it important to have at least one good advocate; I have my GP and two close friends. They can support your decisions and keep eye out for you or be honest with you if they think you're not on top of things. This is especially important for when you get the 'paranoias'.

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Make sure you get advice about access to all benefits. E.g.I receive disability living allowance. This allows me to get some help with cleaning (thus freeing up energy and time) and pays for some 'together time' with my child.
I am currently off full time medication, due to an allergic reaction and am being supervised taking a low dose anti-psychotic (up to x3 per day if I need it), which is keeping me level whilst I let my body take a rest.
Be open, but age appropriate with your child about your illness. Use simple terms to explain what's happening. I would take a regular break (see if you can arrange some 'you time', 'partner time', 'family time' and 'child time' occasionally); it doesn't have to cost anything. Planning a 'break' e.g. evening with a friend, joining a class; anything which gives you a break from parenting. Your child will understand if you don't make a big deal of it and explain that you're having sometime to charge your batteries and give him some time too. My daughter appreciates the independence from me and is growing up appreciating 'her time'.
When you're feeling level, write a list of small goals e.g. Tuesday I will try to do 30 minutes gardening/ walking/ football with my son etc.
I have written a picture book with my daughter about bi-polar disorder for first readers and the very young. If I ever get it published (!) I'll let you know. We have written a follow up for 7-12 year olds.
The only time you need to worry about your child is if you're being consistently abusive in anyway. I feel that children can be very forgiving of a lot of things if you don't overburden them.
If you're still worried talk to your GP or psychiatrist. Regular breaks (even quick 15 minutes for relaxation - for all of you) that your whole family can look forward to (together or separately) will probably help keep you at home, rather than breaking down under the pressure and leaving.
Hope this helps and that I haven't been too 'directive'.