Hello @Courtney27,
It is possible for him to book one of the rooms and another for his mother using his Airbnb profile and payment method.
Strictly, the booking for his mother would be a third party booking as he's the booker but not staying in the separately listed room.
Third party bookings where the booker doesn't stay in your property at all are definitely not advisable and are against Airbnb policy.
You may feel comfortable allowing this booking as he will be in the house at the same time. The only risk is that Airbnb may not cover you or back you up if there was any problem with his mother's behaviour, observance of house rules, accidental damage to items etc. as, strictly, it's a third part booking for a usually separately bookable listing.
Steve.