Re: May I come visit your dojo?
Maybe they had a bad experience or injury in the past. I really think that if someone came to my dojo from another style, they would be really confused as to what's going on. All Aikido really isn't the same.
Also, new students focus mainly on ukemi and our walking kata, which might be really boring to someone with a year or so training already.
If the school was in your own organization, or same style, then I don't see why there would be a problem.