Personally, I'd work on paying those tickets before you worry about driving again. Your license will probably not be given back if you still have unpaid traffic tickets. Also, if you don't pay them, they will eventually turn into warrants and you may end up spending some time in jail. I'd go down to the court and ask about making payment arrangements. They may be able to break it up into smaller payments to make it easier to take care of them.
In California, when you license is suspended, you are entitled to a hearing at DMV, at that hearing, you can explain all of the above to the hearing officer who has the discression to make changes to the suspension (shorten it, allow you to drive to/from work or school, etc). If you have a license from another state, go to DMV to see how (or if) you appeal your suspension.
Keep in mind that if you drive on a suspended license, you are going to accumulate more tickets and fines, you may have your car towed, and you may be arrested. None of those things help your situation.
In the meantime, call your children's schools, explain to them your situation, and ask if they have suggestions on how your kids can get to school (school bus, public transit, vanpool, transfer to a closer school, etc). You could also enlist the help of a friend or relative that has a driver license.