CONSISTENCY is the key to potty training (actually all dog training). Have set times to take the dog out. Right after meals, first thing in the morning, things like that. Try to have it at the same time. Do not punish the dog for peeing (as he won't associate it with the action in the way you want and just encourage fear). Also, try to catch him in the act and make a sharp noise like 'ah' to stop him going and immediately take him out to the appropriate area. PRAISE enthusiastically. My latest pup was trained very quickly with consistency. He was the one I was told would be the hardest to train. He was 10 weeks and I had him trained in a week. His litter-mates still hadn't been trained :patting myself on the back:.
As for products. You can use, in a pinch, white vinegar and a small amount of dish soap in a bottle of water. If you catch it right away it works great. If not, Nature's Miracle Orange-Oxy Power, is also a very good product. The UV light is a good idea because any you don't catch will draw the dog to go there again.
Hope this is of any help. Congrats on the ball of fur. Yes they are cute... just remember that on those days they drive you crazy.
Of course I'm a mermaid... what did you think?