Wanting the dummy is most likely her way of telling you that she wants to be the baby again - the centre of attention. Rather than stressing about getting rid of the dummy, it might be more effective to concentrate on meeting that need for reassurance.
Another idea not previously mentioned relates to this. Misbehaviour from young (and older!) children is the expression of a need. If you work out what the underlying need is, and then meet it, then it will resolve the behavioural "problem". It's not always possible to meet every need kids have (nor necessarily desirable) but in this case I think she is expressing her uncertainty about her place in the family and with you. You can try a type of 'time-in' where you simply sit and observe her play. Give her your full attention, no TV, phones, screens or DS around. Simply give her your attention and provide some comment/commentary on what you observe. Don't ask too many questions and don't direct her play at all or make suggestions. Just be totally interested in whatever she is doing (you can set up the activity beforehand to make sure it's appropriate play behaviour but then just sit back and watch/comment). Don't over do the praise etc. You don't need to do this for very long at all 5-10 minutes should be heaps but it's a really powerful way to re-connect with kids and reassure them they are important to you. Hopefully you will see vast improvements in her general behaviour if you can build this into your daily routine and she will be more likely to be more receptive to redirection of her interactions with your DS.

Good luck!