Apologies, I missed the fact she would be renting elsewhere.
Maybe a bank would accept the fact that she jointly paid your mortgage I'm assuming based on the sale proceeds. But as it's not straightforward a broker might be the best bet.
She might be better off buying as an owner with a property that is suitable under the rent a room scheme, a house with a granny flat attached, with separate door etc, (not detached) that would allow the rent to be tax free under rent a room, and never having to see the tenant.