Julie,
I've done it both ways but the way that works best for me is to send out hard proofs with order forms. The on-line option is OK but if you use a host site, you wait 30 days for payment and my cashflow is bad enough without having to wait a month.
As long as you don't try to shoot formals at a show, most photographers won't have a problem with you. As I've said, they don't shoot candids or portraits (generally) so they shouldn't have a problem with photographers that do. If they did, folks like Gay Glazwell and Christina Freitag wouldn't be able to capture their advertising images at shows.
In fact, I'm going to Louisville next week to bring up my Rottie girl who is trying to get her last major to complete her Championship and while I'm there, I'm shooting a dog that we do the advertising for. I probably won't do any ring shots but we will do some outdoor stuff and some head shots and maybe even some moving shots outdoors.
Have fun,
Jim