A., I can tell you really care about doing the right thing. And you've written a few things that could very well be contributing to what is a pretty normal problem in toddlers, especially when a new baby enters the household.
(1) A great deal of tension around any bodily function tends to create problems. It sounds like this has become a central issue in your household, with plenty of bad feeling all around.
(2) Connecting rewards and punishments to an essential body function often works against success. Natural consequences, on the other hand, will gradually bring her closer to wanting to be potty trained. Don't employ these in a punitive way. Stay sympathetic. As other moms have suggested, if she "simply can't" go some places because of not being able to use the potty, or if she has to go to the trouble of changing clothes and wiping up pee every time she has an accident, she can gradually "discover" that going on the potty would be faster and easier. It's best if you leave room for her to reach this conclusion herself. Kids are smarter than we often give them credit for.
Likewise, natural rewards, such as freedom to go places she likes, are more effective than a necklace, which has nothing to do with pottying. (By the way, if the necklace is something you decided upon as a reward, it may not have much real meaning for her.)
(3) Reward charts and the like can be effective in the short run to interrupt a pattern, but a 30-link chain is far too long to seem possible to a four-year-old. You may as well ask her to pole-vault over your house. If you want to use such an approach, start VERY small: reward a day or two of success. Gradually increase by a few days.
The other thing to remember about reward charts is that the sense of achievement and accomplishment are external. For success to eventually translate into self-esteem, a child has to feel successful and satisfied for herself.
(4) You give her extra cuddle-time for success. Good instinct, wrong message. This suggests to a child that you love her IF and WHEN she is successful. The cuddle time, which I expect she needs desperately now that a new sibling has booted her out of "first and only" place, must be independent of her behavior if you want her to feel secure.
Looking in dispassionately at your whole-family distress, I'd suggest you back off of this issue entirely. It has certainly had at least some effect that you insisted she be trained on your schedule. (This sort of edict has had some pretty dire effects on plenty of children, including a couple of my grown-up friends.) You might offer her the choice of getting back into diapers until she's ready to use the potty. Consider requiring only one or two simple rules: Gotta change into dry clothes if you wet the ones you're wearing. Gotta wipe up the pee. Mention, only occasionally and very casually, that you'd love to take her someplace she loves WHEN (not if) she learns to use the potty.
I'd also be inclined to talk to her about her sibling's place in the family. Express sympathy if she reports any negative feelings. DON'T tell her she shouldn't have those feelings (we don't control our feelings; they just exist). DO say something like, "Yes, sweetie, I can see that is hard for you," or, "Of course you wish I could snuggle with you all the time – who wouldn't love that?" or, "You are feeling sad/mad/jealous right now, aren't you?" Simple acknowledgement of feelings often gives us the chance to process them and move on to something else.
If she seems so inclined (please don't push her), you might follow up with comments about how you notice her delight in or helpfulness toward the baby. Ask her to notice something that evokes funny or tender feelings. Let that sit there next to the sad, confused, jealous feelings. Family love is a complex experience, and contains all of everything. Acknowledging that complexity helps with emotional growth.
Also tell her early and often how much you adore her, every bit as much as the new baby. How glad you are that she's your little girl. How you love her just the way she is, just because she is herself. Don't we all long to know such things? A little kid adjusting to new siblings have these needs much exaggerated.
I really think backing off will get you there faster. Good luck to all of you.