I personally would have used a crate but i suspect you have left it too late to start. Crate training is one of the best ways to stop a puppy from going in the house and isn’t cruel. Also dogs prefer the security of their own space. as far as not havingi him separated from the other dog goes, well that’s down to you. personally I would `have used the crate from day one so they don’t end up being anxious when they aren’t with anyone.
simply put, a dog has to go when a dog has to go and giving him too much room when he’s a puppy gives him the ability to ‘go’ where he wants without it being too close to his bed hence the crate is one of the best ways as they won’t generally soil where they sleep.
The added advantage of a crate is that you control what he chews