It's more kind of do to with getting your head and approach in the most helpful state to be successful rather than a very strict "step by step you must follow this" script of exactly what to do. Some examples which might seem kind of off topic but might help explain the place where your head and approach needs to be (as Zoe said, putting your hard shell on):
- if a LO is told to hold hands when approaching a road but refuses do we just let them run into the road or do we make sure we grab them with a firm grip? We use a very firm voice with instruction "hold hands" "danger!" and at some quieter time during the day away from roads we might explain in a more complex way what the danger is, what the rules are, use toys to role play
- if a child grabs a dog/cat/other child in a vice like grip being friendly or in anger what do we do? Let them continue? Or remove them with gentle but firm hands using the amount of force required but not being mean to them, "let go!" At a quiet time we might practise and role play how to touch with gentle hands, we demonstrate and use safe props to practice with, reinforcing positive instruction "use gentle hands".
- if a child reaches for a hot oven, a glass vase, a sharp object we don't let them continue we stop them "leave it" or if it is more pressing "danger! stop!"
It usually doesn't need shouting or telling off and never needs to involve rejection of the child but it does require the parent to be very firm, very clear and there to be NO leeway or negotiation.
During this SA and your LOs BT routine you are leaving the doors wide open not only to negotiation but you are handing her the responsibility of how things are going to go. Too much power for a LO can leave them in a bit of a tizz as they want you to be in control, and this in turn helps them to feel confident in you.
I would begin way before BT, have a chat, she can understand what you say even if she can't form complex sentences. Tell her exactly what is going to happen at BT and exactly what is expected. Show her with dolls/cuddly toys. Be clear that she is very important to you and you will always always keep her safe and will always come when she needs you. Be clear that she is not to cling to you or you will have to remove her and this might be upsetting. Tell her you don't like it when she clings and you want BT to be lovely cuddles and smiles and happy time so she can go to dream land and have a lovely dream. See if you can get her to agree (doesn't mean she can/will follow through later but you are setting the ground work and can keep practising).
Then, personally if my kid was clinging, he would hear a very very firm voice - "let go of me" and I'd give him a chance to let go nicely but if necessary I'd remove him off me.
The danger of picking up again once she is in the cot is that she will again cling to you. If this repeats I would tell her firmly that you are not going to pick her up at all but you will not leave her. If she can indicate that she understands this and will not cling then you can give her another try (I'd only give one extra try) for a calm cuddle and when it's time to go back into the cot she must go down without clinging, warn her "Remember our deal, you don't cling to me, you cuddle then let go. I'm going to put you down now and I will stay with you, let go sweetie". And put her down. Clinging again, firm voice and remove her. And for me - I just wouldn't pick up again. I'd sit in the room if I had to and I would reassure with voice. "I'm here, you are safe. Go to sleep"
If she stands in the cot screaming at you, again instructions "sit down" (often easier to follow this step first) then "lie down" "go to sleep". I would not tell her not to call you and I would not tell her to stop crying.
I wouldn't hold out for her snapping out of it just because she stays with someone else for a few days. LOs learn habits with different care givers very quickly. My DS was basically forced to learn to take the occasional nap in a pram with my mother, there is not a hope in hell he would ever do that with me looking after him, he needed his cot or the car seat and that was that. Nursery or in-laws can have their own methods of putting LOs to sleep but its *with you* that she has the difficulty and that's partly because you are her primary care giver so she needs you more, plays up with you more, lets out her emotions with you and it's also partly because for a little while you have given in to her demands and she's learned to cry hard and get you to pick her up at nap time and BT and through the night. I'm afraid only you can make this change.
SA is horrible and certainly all LOs go through it, we do need to give them additional time and support at such tricky times for them, but this is where longer term habits can form too.
should I lay her down despite clinging and crying, and walk out then walk right back in to reassure
I personally would not walk out the room. I would put her down and stay in the room.
And I should wait til she is calm before leaving again regardless of whether she is laying or standing?
I think somewhere you said she would stop crying as soon as you walked in and then be happy chatty and lay down. If she is not crying then leave. If she is crying then stay. She does not need to be calm or asleep or even trying to fall asleep for you to leave but she needs to be not crying (shouting in an angry or frustrated voice is not crying, it is angry, this is an example of when I would leave the room and stay outside saying "be quiet, go to sleep". If she calls your name respond verbally or by going in.
Keep in mind there are thousands of parents who cannot pick up their children because they have a bad back of RSI in the arms (from holding children too long) or a disability, recovering from operations or a whole number of reasons. They can usually still deal with SA and be with their child to reassure them without picking up. The love is not less, the care is not less. It is simply a matter of not picking up and working out another way to reassure.
I know this is not an "answer" but hope it helps.
I think if the nap can't move I'd put her to be significantly later. 30 min later than you usually do.