He's desperate to go in and see the newborns, and mum is happy for him to do so, but I'm a little concerned? Is it advisable?

No it isnot. Keep him away from them until they are at least 7wks old.

Not only do jealous dogs kill puppies (not all mother dogs are good or smart), he can drag in disease.

He doesn't need to be in there and he doesn't need to be bothering them.