UAE tourist visa for Indian passport holder

I am planning on visiting UAE with my wife , flying into Dubai and flying out of Abu Dhabi . I believe with a tourist visa , there wouldn’t be an issue with this . And should this info be mentioned while applying for visa .

I am not eligible for visa on arrival, but my wife is , as she has US B1/B2 visa . What would be the best way to apply for the visa . Is it possible to get the visa before booking the tickets ?

Also , would I need to show the proof of stay during immigration , as I ll be staying with a relative in Dubai , and will stay at a hotel in Abu Dhabi .