I have two dogs that are very competitive, how do I get the one to stop peeing on the bed of the other?

give each dog the same amount of attention. I have 2 dogs myself and they are always trying to fight for my attention. When I am petting one I pet the other, I talk to both. Dogs are like kids when you have to kids you have to share your attention with them.

Don't give both the same amount of attention. The dominant one should be petted more and always first. It should get treats first, eat first, go out first, and pretty much do everything first.

You start peeing on their beds, eventually they will stop peeing on beds

Switch their beds while they are not looking.