Your girl sounds lovely
There are others on here with more experience of dogs being possessive who will offer advice.
I’ve not had this issue but have always taken the time to train my dogs to give up whatever contraband they’ve found. If I want to take an item from the dog, it’s rewarded with another item (ball, toy etc) or if it’s a high value item to the dog I may use a treat or bit of food to reward. We practice this a lot when they are young and 8 months is not old - ask her to bring you a ball or toy, take it from her and swap for another item or simply give it back to her, that way she knows that you are not going to just take her prize item each time.......
Dogs natural instinct is to hunt, flush, chase, catch, kill and eat it’s quarry (yes, even ducky toy...) we ask a lot of our furry friends to break that natural instinctive cycle and give up what they have.
With regard to sick - it’s very likely undigested food. To a dog, that’s just a bit more of their meal. Ours eat too quickly and will be sick, the older unspayed female will be sick with hormonal changes, we let them mop it up providing it’s safe to do so and they want to. Dogs are savvy creatures and generally won’t eat it if they are truly unwell. Yes, dogs really are disgusting creatures - fox poo rolling is only really one of their traits! I would only remove the dog from the potential of eating their own sick if I thought it would be harmful to them - most of the time, it’s gone by the time I find the mop/ cloth and clear up what’s left!
I would suggest re-thinking how you are dealing with your dog with regard to possessions. She’s a dog, not a child and even at 8 months will not be able to reason - taking things off her with no compensation may exacerbate this behaviour.
If you are really worried about your girl with your nieces and their friends, I would suggest finding some help from a local behaviourist who will assess both of you in your own home and help with a training plan.
Hope the above is of help,
Jayne