It's an awkward one that's for sure, not helped by the fact the fat holds a lot of hormones and emotions, and people do get sensitive about it.
OP QUOTE: "As I said, I'm confused. She confided in me, I offered a solution we could try together, she went nuts. I'm worried I've offended her. I never started the dialogue about her weight, she did and she brought up the holidays, not me, which is why I made the connection."
I suggest you write her a letter, but get off your sisterly high horse first.
Write to her you would a good friend, and only emphasise how happy you were that she could confide in you, and how glad you'll be when she's able to join into family activities again, and are healthy. Just talk about your feelings about her - not any solutions you have for her and her 'problem'.
However, you have to remember, you are not the boss of her, and it is up to her where she goes with her health /weight for herself.
It's her life after all, and the choices are hers - even if it means she'll end up getting her limbs amputated and going blind with diabetes, having high blood pressure and a bad heart, and almost worst of all, her kids having no memories of her except as someone who lay down all day and never joined in the fun.
BUT it's her life, and her choice to make.
In the meantime, plan your holiday with or without her, but be aware that unless you agree a rota for playing with the kids, she'll probably not join in, and it will be left to you and the husbands. If you're happy with that, then go ahead. If you want to make it more equatable, then you have to get a bit assertive about the time you want 'off' yourself.
If you don't want to see her at all, why not offer to take her kids (seeing as you're looking after them anyway) and then she can return the favour, giving you a break.