Your partner comes from a dysfunctional family system that is built and designed protecting the addiction, and protecting the addict from the consequences of not-fighting their addiction. Unfortunately, this makes you and your daughter outsiders to a very unhealthy ecosystem that will fight irrationally to protect itself.
Everyone involved here has choices, except your daughter, even though to it feels like they do not. You cannot control what other people choose to do, you can only control yourself. Your daughter needs an advocate here or she will be wrapped up in the dysfunction along with the rest of them.
Is it possible your partner would consent to family counseling? You all need a safe, moderated space (preferably with a counselor versed in addiction) where you can talk about how his brother's addiction affects all of you.
You are in no way a terrible person for not wanting to live like this. You just haven't spent your entire life thinking this is normal, or "what you do" for family. His family is not helping this brother or his other addicted brother, just like they weren't helping his father before he died. It is the easier way to just give in and be miserable rather than fight the tide that wants you to let your life and your daughter's life revolve around the addict who continually causes messes and expects others to bail them out of it, but not giving in is the only way to stop this generational dysfunction from destroying more lives.