My husband and I often eat the same meals, but I just leave out the carbs and up the fats. More veg and mayo (and in my case, meats) for instance, as I forgo the spuds he does have. I can cook the same meal, we just don't eat the same portions/proportions. If for instance, spaghetti is on the menu, leave the pasta to her and go for konjac noodles or courgetti yourself. There's loads of work-arounds. Thing is, Slimming World isn't geared to the metabolically challenged... Their diet goes from the assumption that you can process carbs, which you can't. If she can do what works for her, then why can't you do what works for you? You both apparently need a diet that suits you, so... Make it suit.
You mention veggie, I take that it means you do actually use eggs and cheese? Because those can bulk up a meal with fats and protein just fine. Being a vegetarian is difficult when it comes to low carb, high fat, but by no means impossible.
Good luck!
Jo
PS: Did get my cholesterol down on this too. Have a heart murmur, and loads of hartdisease in the family, so not something I'd just gamble with.