Can an insurance company refuse to pay part of the impound fees if they are stalling to settle my claim against their at-fault policyholder?
From what you write, it is not your own insurer, but the other driver's insurer, whom you claim is "stalling." If so, they are not doing anything wrong; an insurer owes a duty only to its own policy holder. The other driver's insurer will not pay out until and unless it either 1) voluntarily decides to, because it believes that fault and damages are so adequately established that it should pay, rather than go to court and lose; or 2) you sue the other driver and win, getting a jugment your favor. Unless another driver's insurer elects to voluntarily settle with you, it does not have to pay--at least until you sue the other driver and win.Therefore, since the other party's insurer has no obligation to you until and unless you can prove liability and damages in court or they choose to settle out of court, they have no obligation to pay your impound fees for you. The insurer's representative is correct; if there's no settlement or jugment, you are responsible for removing your own vehicle from impound.You need to take care of the impound yourself; you can certainly try to negotiate as part of a settlement that the other driver or his insurer pay part or all of your fees, or seek these fees as part of damages in a lawsuit, should you go to trial.