Why not a possibility of flirtation? It doesn't have to be 10 minutes verbal dialog any more then combat needs to involve the players picking up swords and shields and physically playing out combat, live on the floor. Fred the Fighter says he is flirting with the barmaid. "Make a diplomacy(or relevant skill) roll." Success, Fred and the barmaid exit stage left. After which the barmaid asks Fred "My brother is missing, can you search for him Pretty Pleeeeeese???" while batting her eyelashes. Fail, the scene continues with one play path option no longer available. There is still: 2 - the barkeep asking the party to stop the fight, 3 - thinking to complement the cook, and if they fail all of the above, 4 - being hauled to jail for starting the problem in the bar, because that is what adventurers do. (2 - success, the barkeep gives the party a supposed treasure map as thanks, 3 - the cook is out of meat and asks the party if they can please get some more <critter Y> in valley Z, 4 - the sheriff will return the party's valuables when they capture alive Villain Bart so the Mayor can have a public trial and hanging.)Seriously, it's not that hard. Just call a 5 minute bio-break so other players can leave the table and ask the X-card invoking player what triggered it. You CAN and may need to ask that since it may not be obvious. You don't need to ask why they feel that way, just what needs to be changed. And then you change it.
It's not likely to be that one player is a pacifist in a game that typically involves combat like D&D. That's a straw man. Other things, as unlikely they are to be a problem (particularly in a con game - who builds in time for a lot of flirting in a con game slot?), you fade to black or elide over specifics. Rather than steaming plates of meat - it's the entrée. Same thing, less specific.
As for asking the player doing the X-card thing, there are folks on here stating that you can't ask. You are just supposed to change things until you magically remove the objectionable thing or skip over the whole scene. But if the above mentioned bar scene isn't just a whistle stop on the 500 mile rail track but is instead a major switch yard with multiple paths out, you can't just bleep over the bar scene.
As for the spider thing, that should be easy to fix IF you can ask the kid what the problem is. Just sub in a different mini and refer to it as the monster. In this case, it is an easy fix. IF you can ask. (You did have a backup mini?)