It's not uncommon for a toddler's sleep patterns and routine to go a bit loopy when a new baby is on the way. She's probably needing a bit of reassurance which is why she wants the support at bedtime and the extra physical affection.
She's needing support to transition between sleep cycles it sounds like - her pre-baby version of separation anxiety.
And on-top of all that she sounds pretty overtired too as you say.
Are you familiar with BW sleep techniques? You could use a form of walk in/ walk out. Keep things very simple. Have a key phrase: "Sleep time for Carys now. See you in the morning" or whatever and say no more than the key phrase if you can help it. Don't enter into huge discussions at nighttime.
I would say that lying next to her in the bed is a better option than rocking in the rocking chair. By lying next to her - she is at least falling asleep 'by herself' to some extent and it's easier to 'wean' off that but him moving physically further and further away and leaving her when she's more and more awake (that's a gradual removal method if you want to go down that route instead of walk in/ walk out).
For the night wakings, use the key phrase and be physically in the room for a visit but try to avoid lying down again. Mentioning that daddy is tired too could also be part of the key phrase. You could also consider having a chair outside her door where daddy can sit and she can sense his presence but again weaning her off dependence on him.
I'd also change the bedtime routine for a 'fresh start'. You have her putting toys to asleep (also hopefully encouraging a lovey if she doesn't already have one) and you can use the key phrase for them too.
Depending on her understanding and communication skills, you could try a reward system. Focused on if 'she doesn't call out at night' or if she doesn't leave her room until a certain time - you could have a box of toys in there for early waking and buy something like this clock:
http://www.bunnyclock.com/and she can't come and visit you until the bunny has woken up.
I know this sounds a bit wacky but maybe bringing the cot back is an option. I know you wanted to probably use it for the baby but perhaps it was linked to her feeling of safety and the new bed had reinforced the idea of change. I think using a cot at this age would be easier than what you are currently going through.
She may be preparing to drop the nap anyway. She's at the young end of the spectrum for dropping the nap but some do (like my ds). But I expect it's more about leaving and napping alone. Perhaps quiet time could happen downstairs - even if it's just on the sofa. Or you say, "I'm going upstairs to read now. I've got a really good new book. You can come and see if you'd like". And then go upstairs to her room and read loudly - I wouldn't be surprised if she comes up to investigate. Put toys down for the nap etc and have a nap routine too.
Anyway - there's a a few ideas. It's pretty clear you can't go on as you are. I don't think she will be consciously linking any of this with baby but I would expect it's underlying some of this. Good Luck.
