It's not double jeopardy because they're are not the same thing. Your fine of $350 was, presumably, your only penalty for driving suspended. However, your new criminal conduct (driving suspended) violates the terms of your probation and suspended sentence on the DUI.
It's not double jeopardy because the DWLS is a seperate charge - but it also happens to violate the terms of your DUI probation. You should consult with an attorney immediately to see if there are OTHER ways around (or out of) the community service requirement entirely.
Keep a record of the efforts you have made to fulfill the conditions of your probation. The law requires that violations of probation be "willful." If you can show that you made reasonable efforts to comply, you should be ok. It certainly isn't double jeopardy, since the violation is just the continuation of the first case. Good luck.