There's no such thing as "alpha" and "beta" in dog/human relationships. Or even in natural dog/dog relationships. The concept of the alpha, the pack leader, etc, is based on a faulty study done in the 70s of a group of wolves placed in captivity. Since the study, both the original scientists and new researchers have realized that wild wolf packs are familial units, not random members from different families. The head male/female are the mating male/female, not the alphas who have taken that position by force.
While not necessarily related, many people who subscribe to the idea of alpha/pack leader type relationships also use dominance-based training methods to work with their dogs. Dominance-based training is based on aversive methodology (punishment for behavior) to produce results.
Your dog doesn't see you as "alpha" (the primary mating female). Your dog should see you as a source of leadership, guidance and positivity.
What type of training do you do with him? How do you 'correct' him for doing things you don't want him to do?
Not saying it was you, but at some point, someone has scared him. Submissive peeing is due to fear of repercussion and punishment. You should work on confidence building with him, you should work on punishing him for misbehavior, and instead try to redirect him to do what you want him to do instead and praise and treat when he does what you ask. Building his confidence in you and in the fact that you aren't going to enter a room and start beating him will probably go a long way towards reducing the fearful peeing problem.
