Don't just give him a TAP!! I find this very annoying when people say they don't want to hurt their little ponys.. sometimes you have to give them some pain to stop the bad behavior! Don't be so worried!
And I don't think a good solid slap on the backside would even cause a horse that much pain,Just enough to snap that bugger out of his train of thought,which in this case is kicking.
All I can really say is IMO,I think the poster should stick with her current trainer,sounds like he/she has a good head on their shoulders and knows what they are doing and feels confident enough to handle your horse.(from what I have read at least)
Until that trainer can control your horse with no issues,I wouldn't suggest you do any longeing,But I also wouldn't suggest you stop spending time with him.If you say he's fine doing basic ground work,then do it.Just be on your toes,you can't ever drop your guard around a horse like this.I also agree with the idea he has very little respect for you.I would ask your trainer if they could possibly work with both you and your horse with building his respect and confidence in you.I'm sure they would be happy to do so.