Verify Identity on a google account - I've used a phone number once and its too many times

I tried to log into the account and I needed to verify my identity because suspicious activity was detected.

I tried to use my phone number but that has been used "too many times" - fair enough, I have a couple of google accounts.

I then used a family members to get in. That worked.

A week later, the same issue has just happened again - suspicious activity detected (same laptop, same IP, but apparently suspicious?) I used the family members number again and apparently I've used it "too many times". I've used it once!

So do I now need to find another one? I don't have other family members I can ask, so I am now stuck... 

Its an utterly ridiculous and idiotic form of security control. How is getting some random number off the street a realistic means of verifying the identity of the person linked to an account?