D.B.
You don't need to quit your job, first of all. You don't need to make yourself feel guilty about working, if that's what's happening.
It's absolutely fine to continue to breastfeed a 2.5 year old, but if you do that AND co-sleep AND use videos AND give in to her desire for the nanny because you feel guilty, you (and the nanny) have not taught her to calm herself down. A 2.5 year old should absolutely NOT be nursing (or bottle feeding or eating anything) at night. She needs her sleep far more than she needs food.
Does your pediatrician know that your child is awake so much at night??? She is sleep-deprived - for 5 months! - which is bad for her brain development. I understand that a child who is sick may need some exceptions, but your daughter does not know how to calm herself and go back to sleep - she always gets some sort of attention the second she wakes up.
I think you need to read up on sleep training and get serious about this. That does not mean that you let your child scream all night long. It means that your child needs - at this point - her own space, even if it starts with a toddler bed on the floor in your room. If you are completely against her having her own room and her own bed, you need to decide when you think it will be appropriate to implement that! It will NOT get easier at 5 or 7 or 12.
If every time she wakes or stirs a tiny bit, she has a warm body right next to her that feeds her the breast and consoles her when there is nothing wrong (I'm not talking about a raging fever or a nightmare), she is really handicapped in terms of her self-confidence.
This is not a phase that will end. You need to end it by teaching her the skills she needs. That means that everyone involved gets on the same page with how the nights will be handled. You can read up on the Ferber method and seriously get on board. You will have 3 nights of hell and then it will be done. But you already have 5 months of hell, so it should be a huge relief.