Thanks for writing, if neither your new baby nor husband would have been covered under your father’s plan, that makes a huge difference as to whether you can add them to your COBRA coverage. You most likely cannot.
Group Health Insurance rules usually will allow direct dependents or domestic partners to be added to a plan. But when you are talking in laws, and dependents of dependents, that is too far removed. The plan rules will probably not allow the company to add your child or husband.
I wrote a page of COBRA and pregnancy
. The good news is your husband and baby can get their own private health plans and save a lot vs. COBRA. If they are healthy, no reason to pay COBRA rates.
Just put on your zip code in the green box at the top. Hope this helps.