It is allowed to feed the animal non Halal food or Najis meat as the animals are not responsible to avoid non Halal.
You need to be careful that your home or clothes do not get Najis from that Najis food.
You do not need to get rid of the cat. The bowl and all items are not Najis unless you have an evidence that it had wet Najis item in it. If you know that it is Najis, then just washing it with water will make it Taahir.
Muslim is not allowed to feed any one pork oe any part of it, even to those who usually eat it.
Feeding non Muslims Non Halal meat is a matter of debate between the scholars. I advise you to refer to your Marja' of Taqleed.
As jurists say, it is prohibited to buy or sell pig meat, but as for working in a place that serves pork, it is permissible. The problem would arise if you yourself were to prepare or serve the pork, in which case most jurists say it is of obligatory precaution to avoid.
You would need to refer to you Marja' Taqleed for the specific fatwa on this issue.
And Allah knows best.
If it is your house, then you must have authority over what enters it and what happens inside the house. Instead of getting to the stage of disowning, or expelling them from your house, try to get them to compromise.
For example, ask them to cook their non-halal means outside.
Also, continue to do as much dua for them as possible, that Allah ta'ala enlightens their heart and guides them. Remember that the dua of a parent is always answered.