I can see your sticky situation, has the door been replaced/repaired yet? Or have the police fitted a 'temporary door'?
What grounds did they have to believe that he was unable to answer the door/being unwell?
The police should have left a card/notice behind after entry, which should have been given to the occupier as of their Code of Practice: Code B 2011. This card/notice should have contactable details on there, and potentially what grounds they had on it.
As for the legality of leaving him to foot the bill, this is tricky to find out, as if it was legal and they had reason to believe that offences were committed or that injury or damage was taking place/going to take place to persons or buildings, then they are not responsible to foot the bill.. However: no offences , but perhaps reason to believe harm to persons.. Though they were wrong.
I can't find any code of practices which have rules where the police are wrong.
What you're best off doing is, contact the non-emergency line to discuss the matter, or pop down to the police station where you can request to speak to the duty officer with your complaint. Or you can pop into a citizens advice bureaux where they may be able to help you, as this is a civil matter I believe.
If you try all these and are still unhappy, lodge a complaint with the IPCC (Independant police complaints commission) where they may be able to help.
If the door has been fixed or replaced at a cost to your father in law or anyone for that matter, you may be able to claim this money back from the police.
I hope this is of any use.
Adam