Crate him when she's not able to directly supervise, and use a belly wrap when he's out of the crate. Definitely not a testicle issue - this is a training/dominance issue.

Put a training collar and leash on the dog and take him to the spot where he has marked in the house.

The minute he tries to lift his leg give a sharp correction on the leash and a verbal correction.

Neutering will not stop marking. Training will

Good luck