You will need to insure the buildings and you and your sisters name, and note it as a let property. Your sisters partner should then arrange his own contents insurance.
You can get this cover from direct insurers, but you may want to pop into a local brokers office and they can get you some more specific advice. They deal with more complicated queries everyday, and can help you if you need a short term policy also.
I would say that you should make sure that the buildings is covered in joint names as a priority - this is the most simple part as it doesnt involve any other parties and then you have your part of the deal covered.
If it is only your sisters partners belongings in the house, then he can set up a standard contents only policy in his name only. If some of your mother in laws belongings are still in the house I would suggest that he adds your sister on as a joint policyholder to this policy too.
The fact that there is a martgage on the home makes no difference. If you are asked the ownership, you would state 'mortaged' as normal.
Hope this helps a bit