OP doesn't indicate how the babysitting situation came up. How would couple #2 know it's $3 per hour for an additional kid unless couple #1 told them so? They should have told the other couple the total cost per hour, and then either request at 50/50 or 66/33 split. It appears poor communication led to a misunderstanding. Suck it up and don't offer to share the babysitter with them again.
My brother once complained about an invitation he and his wife received about sharing a rental house in the Outer Banks of North Carolina. It was a large house, something like eight bedrooms. Four families were invited. Brother and SIL don't have kids, the other couples do. The "host family," who had four kids and would probably occupy at least three bedrooms, wanted each couple to pay 1/4 of the total cost.
I don't like going out with large groups (over 8) and then splitting the check evenly. It seems more often than not there is one couple who takes advantage, orders expensive items and lots of alcohol, then expects their meal to be subsidized by the others.
That vacation scenario is nuts. To me, the most fair way is to divvy up the costs by bedroom. The houses we stay at seem to allocate the bigger, or master bedrooms logically, assuming families traveling with kids. Like a 5 bedroom house has 2 masters, and 3 smaller. So if one family has more kids, and needs 2 of the 3 bedrooms, they should pay 3/5. My brother and his friends do a per person split. The rest of the expenses are really just groceries, and that's easy to divvy out. We all tend to spend the same amount, and everyone brings some booze.