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Hello. Thanks for the question.
My guess would be that the inappropriate urination is secondary to pain. Dogs that are painful, as I'm sure he is after being hit, may be reluctant to go outside or do any stairs on the way out of the house.
I would want to have him on some good pain relief. I usually go with an anti-inflammatory (Rimadyl) + something else for pain (Gabapentin or Tramadol). This usually gets them comfortable enough to return to normal routines.
My guess is that the urinating in the house should only last a week or two. After that, the pain should be gone and he should go back to his normal activity.
I hope this helps, let me know if you have any other questions.