It sounds like you are in a very stringent box, making it hard to try to introduce new ideas and situations into your relationship.
She wants to be the one to snuggle uo to your back so that she can be the one that decides when the snuggling stops.
I am going to ask a few questions from a woman's perspective so that maybe you will be able to get closer to the reason for her LSD... it may take some time to think through things but once you know what is really behind the LSD you might be able to think of things that will not trigger an adverse reaction.
1- As we age (for women) gravity becomes a cruel trick on our bodies... has she taken to dressing in more form hiding clothing? Looser shirts that hide her shape, pants in the summer when shorts usually are more comfortable, those extra large shapeless t-shirts to sleep in?
If she has been showing signs of being uncomfortable with her body it might explain why she does not want your arms around her and instead wants to snuggle up to you. The thought might also be hidden somewhere in her mind "it is not me, he is just a horndog".
How can you get past this? Random acts of compliments... saying things like "Have I told you that you are just as beautiful as the first time I saw you" out of the blue as an example. Just little things, here and there, with no expectations for results. If it is set in her mind that she has changed it will take a while for her to first realize that you mean what you are saying then a bit longer for her to believe you mean it. Don't go all Don Juan, that will be suspicious, but suprise her with a single white rose (red is so predictable) or a single sunflower (tell her silly can be fun and when you saw it you wanted to share the fun) for no reason, just hand it to her, kiss her on the cheek and leave it at that.
2- Is she using your daughter as a sheild between you to keep you from cuddling... a barrier to keep you away?
She might be thinking that if she watches TV with your daughter that you will keep your distance, especially if doing so has worked in the past. Have you, yourself, made this a tool for her to use?
Ask yourself... what would your daughter do if you joined them... cuddling does not have to be sexual in nature with an agenda in mind... it can simply be closeness. Children that see their parents being affectionate might make comments "eww, gross" but actually they tend to be more secure and have a better chance when they grow up of showing affection to others.
3- When in public (going to the store) is it all buisness with no contact... just two people pushing a cart?
Small things are big... if you walk past her a gentle brush of your hand on her waist in mundane settings, brushing her hair off her shoulder in the check out line and a playful wink as you make eye contact can speak volumes. Physical touches in public, even very small ones, show pride... as if saying "look at her... she is with me!" not only lets her know that you want her everywhere and not just as a sexual partner but will boost her self esteem. (Goes back to number 1)
If you do not go grocery shopping with her... start to offer to go with her. When you go clothes shopping ask for her help "what shirt do you like best?" (a subtle hint that her opionion is important to you).
I don't know if any of this will help or if you have already tried these things, but I will toss them out there.
Good luck!
M- 11 y H- 40 Me- 41 D (1st M) 19 S (1st M) 17 First EA (w/OOW)discovered 2000 Third EA (w/OOW & phone) discovered 02/06 SSM (total) 3 1/2 years