I am also a parent in a blended family. My husband has a 13 year old girl. Together we have an 8 yr old girl and a 20 month old boy. I have known my step daughter for 11 years. My husband and I do not fight often, but this is one subject we do, at times, do not see eye to eye on. All these years, he has always been easier on his daughter then our 2 children. Don't get me wrong, he loves all the kids equally, but at times he will over look something his daughter did, or possibly did and blame our 8 yrs old. Now that she is getting older, he is starting to see a little more. Up until this time, we have had our battles. This is something that has to be discussed between the both of you. If he plays favorite with this daughter, the other 2 are going to pick up on it and not be very happy about it. It happened with my 8 yr old. Then of course we get into the whole routine with my step daughter telling her mother that we blame her for everything and that my daughter gets away with it all. Over the years we have had many a battle. I love my step daughter dearly, but she is very sneeky and she lies alot. My husband is starting to see this, finally. The biggest factor in dealing with and raising children in a blended family is communication. There needs to be communication between you, your finace and your fiance's mother. Trust me, I know how difficult that can be. I have been dealing with that for 11 years. Like my husband, I am sure your finace wants to do "extra" things for his daughter. He may feel guilt or bad for the situation the child is in and him not disciplining her is just one way to help with that guilt. That does not help the child or the whole situation. Talk to him about the way you feel and the way you are seeing his actions.
It is hard at first, but it does get better.