Hey Candice, welcome back! I'm sorry it's under stressful circumstances.
Did a doctor diagnose your lipedema? If so, you're probably lucky - from what I've read, it's one of those things docs tend not to "believe" in.
Either way, that's a tough go. From what I hear, that makes it difficult to lose fat.
However: I'd stick with what you're doing, for the most part. You've described a terrible outcome of veg/nism and your body has a LOT of healing to do. You're gaining scale weight? I would bet money that your body is trying to replace necessary lean body mass. You're also trying to reset your brain chemistry that tells you when you're hungry - be patient with your appetite.
Because of the lipedema, I think you might be one of the people who might benefit from a slight focus-shift from Atkins/high-fat to more of a protein-centric WOE. I like Dr Ted Naiman's philosophy because he does NOT encourage calorie counting or starvation: it's about achieving satiety so that your body can release the extra energy that's sitting there in your fat stores. Cute little mantra: Prioritize Protein, Cut Carbs, Fill in with Fats. He was raised in the Seventh Day Adventist church, grew up vegetarian, and, shall we say, has done a 180... although he's supportive of his patients who still choose veg/nism.
If you're having pain and inflammation issues (your knees?) consider backing off on inflammatory foods. I know, I know, this is too complicated when you've got three kids to look after.
But it can make a big difference. Seed oils are a big one - I had to cut the mayo and commercial salad dressings. I'll save you the novel, but I described it a bit in this
Collagen thread. (That's something else you might want to try.) And I know I beat this horse to death, but if you're not already, try going gluten-free. Atkins/LC gets you 95% of the way there without trying, but you just have to read labels a bit more carefully. Luckily, it's easier now than it used to be.
Good luck, and keep us posted. Hang in there.