L.S.
Although the problem behaviour with your daughter is different than it was with our son, the solution might be the same. Our son didn't have a sleep issue when his sister was born, but had other things - potty training regression, angry tantrums. He was 3.5 when his sister was born. Had been FULLY potty trained for 6 months, was generally and easy-going, really mellow kid. That changed for about 6 months after his sister was born. Started biting, hitting, yelling at teachers, having multiple accidents per day at school, etc. This lasted until he turned 4 (about 6 months after his sister was born). What was strange, was that he NEVER had bad behaviour around his sister. He's really sweet, protective, interested in her.
Our pediatrician said that it's not something kids do out of malicious attention seeking. It's their young brains' way of saying "I'm not getting as much attention as I used to - revert back to behaviour that you did when you got more attention". We tried sticker charts, lots of praise for good behaviour, time outs, taking toys away and earning them back, blah, blah, blah. Nothing helped. The ONLY thing that I felt really worked to break the string of bad behaviour for our son was to spend solely ONE-ON-ONE time with ME (MOM). I hadn't made the connection, since for about 2 months, we had help with the new baby, and my husband also stopped travelling for work. In my mind, our son should have felt like he had 3 times the adult attention as before. What my husband realized was that to my son - it meant going from having me ALL the time, to splitting me with husband, grandma AND new baby. He went from having my 100% attention to having 25% of my attention. Now, we try to do one on one time for a solid 1/2 hour at night before bedtime as many nights as possible (at least 3x/week). This is separate from our usual bedtime routine. We'll do a puzzle, play a game, practice letters, do stickers - but always just him and me. We spend a lot of time talking about his favorite things that day, his feelings, exciting things he learned. We also try to spend an afternoon together one on one 1x/week. Sometimes it's just going for a walk, or going to the park, or playing in the backyard. What's important is that you isolate some time when your attention is completely focused on your older daughter. Baby and Dad do something else - go for a walk, do their own thing. Doing this almost immediately stopped the behaviour we were trying to avoid. And it was amazing - one weekend I had to work and I didn't get to see my son - Monday morning, he had 3 accidents at preschool. We did some one-on-one time that evening, and no accidents for the rest of the MONTH.
The one on one time worked really powerfully for us, and it was surprising to me how quickly he responded. Hope this helps! Good luck!