Help needed for my weeing puppy

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We found a dog outside our house a few months ago. He looked really sweet, but a little thin and after checking him out that he wasn't chipped, we took him in and we consider him ours. He has a problem. He wees. A lot! He wees when we pick up the lead. He wees when we touch the house keys. He even wees when I put on my trainers. He can spend hours in the house not having any accidents, but when he gets excited it just sprays everywhere. Now we thought it would just get better with age, but yesterday my daughter wanted to give him a treat. She put it on the floor in front of them both, and because he couldn't see it, and he could smell another one in her hand, he just wee-ed. It honestly seemed to us that he was just being defiant because he could smell the treat but hadn't been given it (even though he actually had). Has anyone else had this? And if so, what do you do about it. Whenever we tell him off, he wees more, so we tend to ignore this behaviour, but he is getting worse, and now if I call him to me in the house, he comes up to me, wags his tail and wees over my slippers. I'm at the end of my tether with him, but the kids love him to bits. Suggestions please?