Do [U]not[U] initiate a CC dispute. That is a double loser. The card issuer will deny your claim and you will have poisoned that relationship with a frivolous claim.

It was your room and you accepted responsibility for damage. That includes for your kids and for your failure to supervise them.

You say that you "think" that the $261 is too high, but you do not know. You can certainly ask the property to document its costs in: 1) replacing the linens; 2) documenting the damage; and 3) administrative costs. Maybe they will knock a few bucks off.

Who else do you think ought to pay?