Definitely the check out liability insurance issues – as Aecetia mentioned, even if you don’t do it as a formal business or even if you don’t have a tip jar you should disclose it to your insurance company. Ask them point blank if they would cover your kid’s friend coming over and getting beaned in the head the same way they would cover the kid slipping on a carpet in your home. They might consider it similar to a having a pool on your property where it would affect your premiums but you would have piece of mind that you’d be covered for at least casual use by your kid’s friends. I had a friend who was a certified scuba instructor in Florida, and his insurance company made him sign something explicitly saying he would not use his own pool for scuba instruction – I could imagine an insurance company viewing a batting cage in a similar light.

You might also consider upping your coverage level. I’m not that knowledgeable about insurance, so find an expert, and maybe even talk to a lawyer. I wonder if you’d also want the parents of any kid who comes over to use it even just informally to sign a waiver. Again, experts could tell you if that will actually protect you from a lawsuit (probably wouldn’t), but at least it forces you to get explicit permission from parents, and possibly to have a conversation with them about the risks and the importance of kids wearing helmets and following strict safety rules while in and around the cage. Don’t let me take the fun out of this – it sounds amazing and hopefully nothing will ever happen.

As for a formal business or offering coaching, I’ll defer to the experts on how to set it up (and especially what you’d need in terms of business liability insurance), but first thing to check is zoning. As Rustico said, neighbors might complain about traffic/parking. There’s bound to be at least one busy-body neighbor who will report you just because they can, even if the traffic/parking isn’t really a problem. Might also check to see if you’d need to pay for a city or county business license. If you were doing individual coaching sessions, I can’t imagine it would be a zoning problem as it would be much like a music teacher offering private piano lessons (and presumably you are dealing with one car dropping off one or two kids at a time). But you never know, and even for that scenario you might need a business license.