Wife: advantage or drawback when asking for visiting student position?

Be honest. Present it as a happy coincidence. That's what it is, after all. For example,

I've always been interested in different research communities and paradigms, given how this knowledge can help me to work more effectively with others and to introspect my own methodology. My wife has been offered a place in [state] also, so this is a ideal opportunity in my academic career to gain the experience I've sought.

I don't think professors would be more likely to accept you out of empathy if you're expecting them to fund you.

On the other hand, there might be a question of how serious you are about wanting to go for research purposes, particularly if your work is not very close to theirs. But if your work is not so close, they probably wouldn't accept you anyway.

So I don't think it makes much difference, but just to keep things brief and straightforward, I might omit mention of your wife in your initial email. (Actually, if you don't know these professors but your advisor does, it's probably better if your advisor contacts them first.)