OP, I think you are probably overthinking this.
There are two separate tasks going on here. You are babysitting, like you normally do, and your BF is doing the trailering. So:
- you charge whatever you normally charge to babysit these kids at shows.
- he charges for trailering. I’d use your trainer’s $150 as a benchmark-- since that is the “market rate” --but then subtract a bit from that since there’s no wear and tear on his vehicle. Let’s say make his fee $100. That’s $10/hour (4hr to show, plus an extra hour to go get them, each way).
And then ask you BF if $100 is enough $ to make this worthwhile for him. Bump it up, if not. If they balk at paying that much, then then it’s not a good match.
Know that they probably value their time much higher than $100-- obviously they don’t want to give up a whole day to go to this show, so $100 will seem like a bargain.
This may cause you to say, hmmmm that means we could have gotten a lot more than $100, right? But these are trusted employers who you seem to like, and it’s not good business to gouge someone at higher than the market rate, just because you can. So just decide what number makes it worth it to your BF, and go with that.
As for Gas expenses, the simplest solution would be for them to give you a $100 pre-paid gas card, which you just return with whatever balance is left on it.