I've been here for more than 18 months.I wont advice you to go to big cities.The hustles and bustles there are might be unbearable for you to cope with.
In my opinion,a fairly big city or medium size cities would be ideal for a mother like you.
If you negotiate well,your salary in this medium sized city can be 100 rmb per hour and if you're good enough to muster up enough classes,then you can be netting in 8k rmb every month and expenses in medium sized city are not that much.
Take for instance my humble self,i net in about 8-9 grand every month in a small city and i spend only 1k every month though i'm not the freaky outgoing type but i socialize once in a while.
Mind you there might not be too many interesting places to hang out in small cities but its cool and i love it.
I can link you up with nice schools in my city if you don't mind.
Hope you'll have a wonderful time in China.