Hello! I have been meaning to reply to this for a couple of days but never got a moment. I worried about this too - my daughters are 6 (just) and 2. I didn't worry about explaining to the youngest but having watched my own Mum do loads of weird diets over the years I was anxious that my own weight loss shouldn't negatively affect my daughter. I explained to her quite simply that I was carrying more weight than was healthy and it was getting uncomfortable for me and this was a good, doctor-approved, way of sorting that out. It meant Mummy was going to be eating some different soups and things for a while but would go back to usual eventually. I also explained about the groups, and when I had a couple of "pop-ins" she was interested and asked to come too and met my LLC and saw what it was all about.
I always try to be frank with my children (within reason!) as I think euphemisms and being awkward etc can cause more difficulties. She has totally accepted what I did and has at time been really sweet and supportive too. (Tells me I'm looking "taller"!!)
Good luck!! Hope this is useful!