Oh Kelly, it sounds like you are having a tough time at the moment. I really hope you find a way out of this that makes everyone happy.
I have tandem fed twice now. I had the skin crawling, get me away from this feeling when I actually tandem nursed so I had to stop that 8 weeks in (it was either that or wean DD1). I have never actually tandem nursed with DD2 & DD3 in the 2+ years since DD3 has been born. This has limited the nursing aversion but I still feel it from time to time.
Have you tried distraction to help with the feelings? Not distracting your toddler but distracting you - I found having my laptop to hand, a book, calling a friend, eating playing a computer game helped to take my mind of the sensation of nursing which seemed to lessen the feelings of 'argh get off me'.
You could try distracting yourself for the feeds she really can't do with out and work on eliminating the ones she can do with out (at times I turned on the bedside light and read for early morning feeds even though I could have done with more sleep!).
Do the feelings happen when you nurse the baby too or just the toddler?
It could be she feels she is losing you to the baby so is clinging on to the one thing that makes you be with her - nursing - no one else can do it but you and the more you push her away, the more she is trying to nurse. If she wasn't bfing she might be demanding to wear a nappy and have you change her every 5 minutes or insist you spoon feed her on your lap when she can use a knife and fork.
I know part of my frustration was down to DD1 backing off from food and exclusively nursing for 2 weeks when I needed her to be a big girl and be more independent and not nurse so much, of course she was only 20m and nowhere near be able to do/be what I expected.
I still have unrealistic expectations of her - I had a burst ovarian cyst at home (I didn't know why I was in so much pain though) and she made me lie down, got me a pillow and blanket, got the phone to call DH and entertained her sisters (3.11y & 2.1y) in the playroom while I groaned on the floor on the landing.
Whilst I am ever so proud of her and have told her this - I was talking to a friend about it and quipped that I wished she not let DD3 play with a tub of sequins which got emptied all over the rug. DD1 is 5 not 15!! She did an amazing thing that afternoon but I just set the bar too high for her. I've not said any of this to her though.
Is it part of being the PFB that the expectations are set high and by the time the next child reaches that age we realise just what they can/can't do so cut them some slack or perhaps I am just a hard task master!