I agree with Out - most tension for SMs comes from a well meaning but misplaced 'you are not the parent so butt out' attitude.
As a SM you are forced into a semi parental role, whether you like it, whether the kids like it. Because you are the adult, you are the provider, it is your house too, and the child is still dependent. Ignoring that is just not workable.
Having said that - it's not the same as a parent. You haven't got the same ability to influence, big life decisions or schooling etc are all your DSCs parents responsibility, not yours. And you may meet resistance from a resentful 'you are not my parent' attitude from a confused child who will look to their own parents first for rules.
So it may be wise to step back from as much as you can stomach, but set a few simple rules to your DSD that are about the house - actively ask for her cooperation and talk to her as much as you can - explain that you know that you are not her parent, you know her Dad is pretty laid back, but that there are some things that are important to you and it is your house too - the one that I presume you pay for, you clean, you manage. Treat your DSD as an adult, respectfully, but keep constant on those few rules and keep telling her the reasons why it is important to keep tension low in the house. It really is worth doing some nice things for her regularly to let her know that as well as rules, that you also care about her.