Thats classic poor surface prep.
Cement board etc should have been used, but more often than not it doesn't get done, guys just
tile straight to the floor and these cracks occur.
You can't really rectify this without lifting the floor, the timberwork needs to be checked for strength and 'bounce', re boarding, which will add about 15mm to the floor, which in most cases won't effect the kitchen too much, just plain down the kick boards, plain the bottom of the doors and get a cabinet maker to make a hardwood threshold strip for the door.
It's a shame you will have to do this, but the problem should be sortable.