You are using more than one parenting tool for punishments, which is great. I'd like to suggest some others for you to try which have helped me and why they work for us.

Smacking - doesn't work for us at all. In fact, DS likes it so much he'll come up to me and ask me to smack his bottom then complain it wasn't hard enough. He is a strange child.
Time out - only starting to work now, tbh. He's old enough to understand the need for thinking time.

Time in - when Liebs was upset about something, I would hold him and talk him through his feelings. Tell him that he was upset because X, however Y has to happen and when he calms down we'll do Y then Z, which he enjoys. Didn't work immediately. The first time it did work I remember clearly: I was dropping him off at Nursery, age about 2.5, and they had an animal day. His carer had brought in her pet rabbit. Liebling liked the rabbit, who was outside in a run, but the fence outside wasn't up so I couldn't leave him outside and go. Liebling had to go inside and was very upset. So I told him "I know you like the rabbit and want to stroke the rabbit again. It hurts and upsets you that I've taken you away from the rabbit, doesn't it? The rabbit is a lot of fun. I understand that. But there isn't a fence up, so you have to stay inside for a bit. You can eat your second breakfast while the fence goes up then, when T says so, you can see the rabbit again. The rabbit will be here all day. Do you understand all that?" Tears dried up, he ate his food happily and was manageable again. We'd talked through his feelings, I'd acknowledged them and suggested an acceptable course of action.
With your DD, I would say something along the lines of: DS is allowed a dummy in the day and you're not. Does that seem a bit unfair? Well, DS is sleeping now and you do get a dummy to sleep. DS is just a little baby and needs lots of sleep, so you'll see him with his dummy more. When he's bigger (insert other compliments if you like), like you, he won't need it as much and won't have it. And when he has his dummy and sleeps, we can do other things, such as *insert activity choice here - colouring, towers, baking, sweeping floors... something with a time limit, even help with a chore!*. Once time in is working well enough that your DD can do this for herself with minimal prompting, that's when time out really works wonders as she knows what she's supposed to be doing during that time.

Another technique is distraction, so if she starts on a dummy fix tell her it's a pity she wants a nap now as you were going to do XYZ that you know she likes.

You can also talk about stories, a story of a big girl who needed a dummy (maybe the "big girl" being a mummy?) and how silly the girl looks and encourage her to outgrow the dummy that way?