Hi S.!
You have a tough situation on your hands. No matter how hard you try to allow enough time for your daughter, she will always feel like you LOVE him more than her. This is what you will somehow need to overcome.
It's easier to "disrespect you than him" that is why she listens to him. If she yells back a him, then YOU will be mad, and she will feel like you love him more than her. She avoids feeling this way...so she listens to him.
I am a stepmom, 1 boy and 1 girl. Have been for 13 years, now. I remember my stepdaughter HATING me for no reason at all. I gave her quality "girl time", bribes with presents, watched her favorite shows with her....all to make her HATE me more! Then~! she began being nice to my face, but when she went to her mom's house, all she would do is badmouth me! Her poor brother was in the middle of it, always defending me.
It's so difficult to successfully "blend" a family, and the only words I can give you is LOVE and PATIENCE. You are going to have to "change" things in your home to make her feel just as loved as she was before your new man. I made my husband do this with his kids. I think it was the "key" to adjustment. She may need you to lay with her at night for a little bit at bedtime (read a book or watch TV). Maybe a once a week dinner, just the 2 of you, at her favorite place. If your new man is as wonderful as he sounds, then he wants what's best for you AND your daughter. This may NOT be including him in certain situations. I know you are trying to make a "family" together, but you need BABY steps first to be successful. If you've tried things like this, and you're back to square one, then try again. She will eventually accept him, maybe not admittingly, but will.
You didn't mention if she see's her biological dad, or not. If she does, then it would be normal for her to "play it perfect" in your home, then turn around and say mean things about the "new man" to him. These will be things you'll have to figure out as they take place.
In my situation, I played "cool stepmom, friend" most of the time. Before I disciplined, I always reminded my stepkids that their "dad was at work, so I'm in charge, please don't make me the bad guy, cause I love just being FRIENDS with you". I always made it a point to tell them that I was NOT trying to take their mom's place in their lives (without coming right out and saying it). Even though we had the kids 1/2 the time, and I WAS the mom, I had to act like I wasn't in order to "begin" a trusted/loving relationship with them. It's VERY hard.
Too many kids are expected to adjust to 2 moms and 2 dads now-a-days....it works for alot of families, but it doesn't work for most. Plus every child is different on their expressions and handling situations like these. If YOU want this man in your life, then it is assumed that she HAS to like him (she probably does.), but it's not as easy for her as we would like it to be.
Today...my stepkids love me so much. They are 21 and 23, and are out of the house. They send me BD cards, and call me "out of the blue". I am being rewarded NOW, for my love, patience, and hard work THEN.
Even if you think your ideas are not working, give her love and patience, and especially quality time. She'll come around. It just may take VERY long time!
Good Luck :o)
N.