My advice is to just calm down a little. Ok so your teenaged daughter wants to be gothic- thats normal. She is at the age were she is needing to be like others that are around her. Just because she dresses in all black doesn't mean she is doing drugs or something worse. When you are on her case (and your ex's case) about how she dresses, that just pulls the two of you more apart instead of making this very hard time between a mom and daughter a little easier.
I would be mad if my husband told my kids to not listen to me. My ex never does the same bedtime or anything with our 2 kids. But I look at it like this, when they are at their dad's I know they are not going to get any sleep, I know that they are going to be tired the next day or two. So instead of fighting it and complaining to my kids or their dad, I just prepare an easy dinner the night they are coming home and have them go to bed- sometimes even let then stay home from school to help make up on their sleep.
About the no respect thing. I teach my kids to respect themselves. I think that you and your ex both have good arguements. My husband and I were just talking about this just last night, we don't want our kids to listen (respect) to adults just because they are adults and end up getting hurt. Example: child predetors, I know thats a bit much. But we teach our kids to stand up for themselves and if they have to to rude- be rude. We do not want our kids to be a doormat to anyone.
I hope this helps and I know this is a hard time- single with teenage girls. Just remember when you were a teenager. Try to help them, not mold them into a person they are not- they will only hate you for that.