Not to rain on your parade, but you may be getting ready to bump into another headache- if that is a stripped lower.
A stripped lower that is more than 80% complete is a firearm- legally. It is not yet a rifle nor a handgun- it can be assembled into either one. On the form 4473, it is an "other".
Federal law says that a dealer can sell a rifle or shotgun to a person at age 18. But all other fireams, you must be 21.
If it is a completed upper, with stock, it will be a rifle on the 4473. If it is 80% or less complete, it is not a firearm.
As far as parents desire- sorry- their house, their rules. If you want your own rules, find your own house. Does not mean I agree with their rules, but what I agree with does not matter- not my house.