EV, Home Energy, & Child Tax credits

We bought an EV this year, we have 1 child under 17 but only have 4K in federal tax withholdings. I want to install insulation this year before for the up comming winter heating bills start to hit but don't want to lose the credits.

 

I realize I don't have enought tax liablity for the full EV credit and that won't get carried over and the home energy credit would BUT would I get the child tax credit on top or would I lose that credit too? 

 

Is this math somewhat correct?

4000 Tax withholdings + 7500 EV credit (lose 3500 for not enough liabilty) + 3600 child tax + 500 home energy credit = 7600 refund(ish) with 500 rolled over?