HI -- hang in there! I think a lot of us are going through similar issue with this age child (I was just searching the board for help on random early wakings). Regarding the taking your LO to bed, remember what Tracy says..."start as you mean to go on." There's a great summary of approaches here at this site:
https://babywhispererforums.com/index.php?topic=63896.0Whatever you choose, I agree with Sasha's mummy that you've got to be consistent. It's so hard when you're sleep deprived, isn't it?! One thing that helped me was to review the plan with my husband before going to sleep. We'd remind ourselves what we would do if there was a waking, and then if it happened, it helped us be strong with whatever it was that we were going to do. I've found that if I just react when I'm tired, I almost always do some accidental parenting thing, so thinking it out ahead of time while I was still awake has been really helpful.
Also, when our LO was transitioning to one nap, we found that it really affected the night sleep, and he had previously done so, so with yours who has struggled with that since birth, it might be very confusing for her to have different wake and nap times each day. When they transition, they sometimes do need two naps depending on when they wake up, but maybe you can log her sleep (bedtime, wakings, and morning wake time) and compare that to the nap times at her nursery and see if there is a pattern. Keep us posted!