I truly don't know what is fair and what isn't in this case so here are the facts:
I carpool with relative A to work every day, I am right on their route (there is a 200 Ft side street they have to pull into to get me).
I am charged about $25 for 15 trips at about 3-4kms from our destination (one way), keep in mind there is 0 extra mileage for them. Their car gets about 35 mpg
Relative A hit an obstacle on the road (on my small sides street) one day on the way to work and incurred $800-$1000 worth of front body damage.
Relative A now declares that the $25 does not cover damage on my small 200 ft detour and the right thing to do is split the repair...
I don't want to get taken here as Relative A is generally always pulling at my heartstrings and getting money out of me but I also want to do the right thing or at least what most people would consider fair.
*The repair is mostly cosmetic but could over several years eventually cause further wear and damage to the vehicle which is 5 years old.
Please help.
Throwing the repair into it, just muddies the waters. At the base of it is that your relative has not been charging you enough for their inconvenience.
If you were cycling to their home, and waiting for them while they finished breakfast, then left together, (only you are the one waiting) maybe your amount is fine, but picking up someone else is a hassle, and doing it routinely should be compensated. When I carpooled, this is how we did it, and i only paid half the gas. Think of it this way, what if every day you picked up their kid from school and walked them to your relative's home. (assuming you were close by) you were only walking, so it is no cost to you, but wouldn't you like a bit of money for having to be responsible all the time, but would do it for free if only occasionally?
Around here, regular carpooling costs START at a little over transit (bus) fare, for convenient routes. e.g., $5 per trip or $10 per day (round trip). This is between private individuals, and similar across a lot of different groups. Transit would cost about $3.75 per trip.
My two cents would be to acknowledge their angst about the repair and suggest to increase your carpool rate to $5 per one way trip. (or whatever you decide). OR, offer to get yourself to their home to leave together in future.