If the landlord does not at least help to pay 50% of the cost to heat treat the house, can we sue for the entire amount?

My sister recently started renting a home on March 4th. Within about 2 weeks, she started noticing bites on her five children ages 2-10. Within another week, she started visibly seeing bedbugs. Prior to renting the property she specifically asked the landlord if there were any bedbugs in the home and he stated no. After it became obvious that there were, she texted him pictures of her children's bites and of a bug. He started using a service to do spray treatments. The contract states 90 days to get rid of them. They are twice as bad now. Bites are so bad on her kids now that the daycare asked her if they were sick. She asked him to try heat treating the home to get rid of the bugs. I called him and offered to pay half of the cost. I own the house that my brother lives in and once he got bedbugs (friends had them and did not tell him there were bedbugs in their home when they were coming over) I had the house heat treated. End of bedbugs! No more and it has been over 6 months. My sister's landlord will not listen and will not agree to even pay for half of the heat treatment. He insists that since the health department gave him the recommendation for the company, that they are responsible. I have scheduled another company to do the heat treatment next week on June 4th. I cannot have my sister and her kids being eaten alive by these bedbugs. The landlord needs to take this next step to remove the bugs but will not. The landlord is now trying to blame my sister for bringing the bugs. Her previous landlord (where she lived for 3 years prior) has agreed to sign a letter stating that she left the previous home with no bedbugs. I hope this is enough proof. I am not sure what else to do to help her.