Mobilityare far from poor so I wouldn’t worry about that, nor do they think of us “who would need it” when making substantial charity donations. I wouldn’t let this worry you.
I take it you want to stay on the scheme. If so, the first thing I would do is to get mobility to put you in a hire car more suitable for your needs. I would then tell motability to pay my advance payment on a nice car of your choosing thats available on the scheme.
A cash payout should be based on inconvenience, Anxiety caused delaying your appointment, anxiety of being called a liar, anxiety over saefty of your daughter. You could also take into account service at the dealership and being lied to and they all have physcolical effects. I wouldn’t like to put a figure on this other than I expect it to be in the £1000’s