I suspect if you have a big "clean-up", it will be a mess again before you know it. Running out of heat, dog feces, and lice indicates to me that the kids are in jeopardy. I hate getting involved with the government, but I would call Child Services. You may need legal protection in case your sister demands her kids back. File to be their foster parent so you have legal oversight and financial reimbursement. Your relationship with your sister may suffer, but the kids health and well being comes first.
Good luck!
Inchworm
Good luck!
Inchworm