Yikes! The first responses are a bit... weird!
It is normal to still be bf at 2, and also to bf to sleep. That's not the problem.
I agree that your dh and many pp seem to think that the problem is YOURS to solve. And that's the issue. Because you bf, you've got to solve how to settle her when bf doesn't work.
We took it differently. I bf all mine to sleep (till 2 or 3 depending on the child), and when it stopped working, as you describe, and they would still be awake we started a new routine. I'd bf them, if they fell asleep quickly then great, but if they didn't, he'd take over and sing/ tell stories in the dark room until they either were sleepy enough to put into bed, which he would do, or if they became tired and unsettled, I'd pop back in and do a final quick feed and put them into bed.
So gradually it shifted over to the new routine as they learnt they didn't need milk. But it took both of us doing our bit to get that to work. My dh didn't just say bedtime was my problem and would only do it if it involves nothing other than plonking a kid in bed!
Routines and habits can be changed gently and successfully if you're both on board. No need to put her in her bed and just leave her, which would be a big change from bf to sleep.
All mine are able to be put in bed, quick story and song, then lights off and sleep now. So bf to sleep as toddlers doesn't ruin them for life ;) mine are now 7, 4, 3 and youngest still feeding to sleep at almost 2. Oldest 3 all asleep in minutes on their own.
But again, totally normal to still be bf at 2! I've lived in 4 countries with my various babies, and the UK is the only one where bf is seen as a weird and unnatural thing.