Do you run G-Suite for your family? That would be the only reason I can think of to not be using a personal account for this purpose.
For a while you could get a free google apps account for up to 10 users. A free google account + your own domain name which costs you less than 8 bucks a year.
If they were smarter maybe they would just offer this as a paid feature on top of gmail. Its not like it costs them more money to deliver email to a different domain.
I _think_ (not entirely certain as the docs are pretty bad) that the very-recently-accounced Google Cloud Identity free tier does almost that for free; but it's just the identity service, and doesn't include any apps like GMail. Not sure if it has mail routing settings, or if that's just standard DNS.
Because of these issues I abandoned moving my family to G-Suite I had setup and instead use it for forwarding to our free Gmail. Not sure if we're missing out on anything much we would've had from the free tier of G-Suite.