OP is correct.
A couple of comments:
1. $1400 of the $2000 CTC is refundable, meaning you can get it back even if you don't owe the tax.
2. The CTC applies to kids who are under 17 throughout 2018. OP is probably OK.
3. There are other juicy tax credits for someone with that sort of low income: retirement savings contribution credit, earned income tax credit, ACA subsidies, and cost-sharing reductions for ACA Silver level plans.
4. MFS is quite often not the best filing status, but OP probably knows that. MFJ, even if the couple is heading for a divorce, might be better if the parties can cooperate.