First of all, congratulations on your imminent promotion to a DAD!
I'm no expert but be careful before you attempt to kill 2 birds with 1 stone. Consult one of the ATPL providers and speak to your CFI to see what practical options you have.
I am mid way through my ATPLs and was a dad when I started. Sure it can be stressful but then again so can many other things in life. I've found a comfortable balance between family life and the demands of the ATPL course, bottom line .... it can be done. So good luck and all the best