Isn’t it fortunate that you almost certainly won’t be in your current economic bind for very long? Maybe a year, or two, or at most five? Then your kid is in full-day public school, you’ve got that many more years of seniority at your job (and probably even a promotion or two at that point) so your salary will be higher.
I forget the exact numbers, but I believe the average time on welfare (in the U.S.) is well under 2 years over an entire lifetime.
Isn’t it great there’s a safety net for children who have it much worse off at home than yours does?