Direct answer -- of course this is my opinion and based on what you supplied here - you are wrong.
She might not have made the most appropriate decision to invite him but I can understand why she got upset at you. At this point she, on a whim it seems, invited him. To dis-invite him after just asking him to attend would be down right rude. Who knows completely why she invited him on a whim - there was an extra ticket? (I would have done the same thing); she felt maybe it was a way of thanking him for the previous years in which he coached her boy?
It could be a million things that have nothing to do with him being attractive. She may have been talking with him in private to thank him for being a good role model for her son, or her son really liked having him as a coach or hey how are your other kids and wife? It could have been sorry if my boyfriend acts weird - he is a bit overprotective and jealous so he may act rude towards you.
This would put me over the edge as well...."I pull her aside and say to her we can walk down and get the kid but hes not coming to the party..." My respond would not be much different than hers ... what the heck you are dictating to me what I can and cannot do! I am an adult don't tell me what I cannot do.
And I agree if she invited him and then 10 minutes later said no sorry you can't come - it could cause a scene.
Sorry buddy you are too over-protective and untrusting and insecure. If you have a girlfriend you love - you need to trust her and not give ultimatums especially over something so small as this whim of an invite.
Now unless you have something else to go over this invite to a former coach of her sons done a whim - this is out of line. Your girlfriend is going to be exposed daily to attractive men so from what is written on here she did nothing inappropriate other than invite two people (this former coach and his son) to a team party. For that matter what are you doing you there? You have even less association with the team - you are not the kid's parent and unless I got this wrong - you are not directly involved with team - a team member or a coach so maybe you are the one that should not have attended this event.