What type of bottles are you using? Are you using something with a nipple shape that is comparable to yours? Try getting as close to the size and shape of YOUR nipples as you can and she'll have an easier time going back and forth. A good place to start is Playtex Natural Latch.
We tried nipple shields, etc. but in the end, as she was getting closer to "getting it," I got a scale from a lac consultant and made her wing it. That way I could weigh what she was getting at the breast. If she didn't get enough over the course of a few feedings we topped off with a bottle as needed. Following her lead for a few days, literally glued to her in my house, we figured it out together and she figured out she could nurse as much as she wanted, whenever she wanted. No more waiting for a bottle and being forced to finish 4 oz. or whatever, she loved it eventually! That'd be my biggest advice... nurse her on demand as much as possible. If she even looks hungry, give her a boob! You say she latches great and knows what to do - let her do it! If she falls asleep, it's ok - she's big enough now, she will wake up when she's hungry again. If it's in 10 minutes, fine! Put her back on. I see you have older kids and it can be hard to juggle - but if you can even get someone to help out with them for a couple of days, and let you just focus on getting the rhythm with your DD, you can be 100% successful.
You ask -will her suck improve? YES - if you give her ample practice at it. Letting her laze it out with a bottle most of the time won't improve her breastfeeding of course.
We had to learn that too. But this is where getting a bottle nipple that's closer to YOUR anatomy can also help. That way there is less difference in how she has to "work" the 2. And something that is closer to you, like the Natural Latch, will be a little harder for her to work anyway - which is the practice she needs to eventually transfer full time to you.
You ask - are you doing something wrong, NO! Should you keep offering the breast - YES, if she knows how to latch, for every feeding offer her the breast first. No bottles first! Seriously look into getting a scale so you can weigh her before and after feeding so that *you* can be assured of what she's taking in from the breast. Most of the time your insurance WILL cover the cost of a scale.
It took my 30 weeker 3 months to learn to nurse exclusively. Now, she was in the NICU the first month, but still, 2 months after we were home. It was a long road but very worth it. Keep sticking it out - it CAN work! Perserverence is the key here. If your goal is exclusive breastfeeding, then it can 100% be done - just keep your goal in mind at all times and think about how you're going about things. You know your baby best and what she can and can't do right this minute, but I promise you, you can get to the point where you are exclusively nursing her. If I did it, anyone can.