Yes, you can go to jail for failure to comply with the court's order. It sounds to me like the Court already took into consideration the fact that you are a stay-at-home mom by ordering you to perform community service instead of serving jail time. You may be overplaying your hand by relying a little to much on the single mom argument. (You are not the only single stay-at-home mom who has come before the judge.) I strongly suggest when you return to Court on the 19th that you ask the judge for a second opportunity to complete the court-ordered community service.
The best way to stay out of jail is to get a babysitter this weekend and get as many community service hours completed as you possibly can; show that to the Judge, and ask for more time to finish. Other than that, you can ask for an extension on your probation, which, unfortunately, will also extend the other conditions of probation (e.g. monthly reporting fees, UA, etc.). If you have no time, but can get together some money, you may also ask the Judge to amend the conditions of your probation so that you can pay an additional fine in lieu of the community service hours originally imposed. Whatever you decide to do, make sure you have a plan in advance. Simply telling the Judge you're a stay-at-home Mom probably won't get much traction. It's a perfectly legitimate reason for falling behind on completion, but not a "legal excuse" for failing to comply. As a last option, you may also ask the Judge, or hire an attorney to ask for you, to unsatisfactorily terminate your probation.
You should hire an attorney or immediately contact the Fair Defense Act in the Montgomery County Courthouse in Conroe, Texas. Many of the judges in Montgomery County are willing to work with someone so long as they are proactive in taking care of their problems.