I would say obedience class, or an at-home trainer or behaviorist for helping you with personal troubles like the cat, nipping, etc.
As far as the peeing goes-I would get bloodwork done. My cattle dog has had a "peeing problem" since I got him-he's 9 months old now, but always had to urinate frequently (every 1/2 hour) and thus causing accidents in the house. While we were doing the bloodwork and other things, diabetes insipidus, Addison's Disease, and kidney failure were the three things we were looking out for. The bloodwork showed no signs of any of them, we gave him measured amounts of water and his urine concentrated and no accidents happened-he was actually diagnosed with polydipsia, he just drinks too much water. So although everything IS checking out okay with the urinalysis, bloodwork should be done to rule out anything else (such as the kidneys, etc). The urinalysis should be showing whether or not there is sugar in the urine, which could be a sign of diabetes. The bloodwork is usually about $100 and well worth knowing what is going on. I would talk in depth with your vet about the problem, there could be a number of underlying causes not visible by simply a urinalysis.
If all else fails, is he crate trained? You may need to go back to square 1 and re-housebreak him, have him in his crate when someone isn't supervising him. When you have him out, have him close by or tied to you with a leash so you can catch him before he goes and usher him outside.
I wouldn't rehome him. Having a dog without problems is hard enough to find a home for-if he continues his problems in a new home, they may not have the patience and may be continuously passed on until he ends up at a shelter (where he may or may not find a home) or until he ends up on a chain in someones backyard.

Unfortunately, that is how a lot of "problem" dogs end up.
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