I can totally understand your frustration, and the billing for each (mom and baby) is likely correct. On the bright side, the baby's deductible is almost met for the year and it's only May, so while it's more than you expected to spend now you would have probably paid most of it anyway.
In addition, most policies have a total family deductible, so if you're on the same plan, check the fine print. If your family's deductible is $7000 and mom and baby have already paind $6900, you and any other kids probably won't have any charges for the rest of the year.