If sounds like this was a stray cat in whose previous life experience food was an uncertain and precious commodity. So, food guarding is a pretty natural behavior.
Once she is spayed and a little more grown up and used to the fact that food is always available to her at her new home, things will settle down.
I had a Callie whom I adopted from a shelter at about 7–8 months old and she was just wild with tons of energy to spare. She was constantly flying around the house and irritating my resident cat.
But once she hit the 12–16 month old mark, she settled down into the most peaceful and good natured adult cat. Out of all the cats i’ve ever had she turned out to be the most stable and less weird in personality than any other cat.
But none of this was in evidence during her wild kittenhood. And most kittens are crazy anyhow. They have more energy than they know what to do with but once they settle into adulthood, it’s a different story.
However, any young animal plus toddlers is just not a combo which should EVER be left unsupervised. Perhaps you’ve been fortunate to have only had very placid cats in the past (but how were they as kittens?)
But even the most calm cat can respond badly to the sudden unpredictability of toddlers. And with two of them, you’ve got your hands full just with them.
Until both kids and kitten grow up a little it’s probably best to keep them separate as much as possible with only short periods of time interacting with each other.
Could you place kitty in one of the bedrooms while they are visiting? As long as she has her litter box and water and kibble, she should be fine. Of course the kids are probably going to want to pet her and play with her so maybe some supervised playtime along with some toys for her to chase as well as an adult right there would be fine and then give her a break in her own space?
Do you have one of those fishing rod/feather dangly toys? That would be great because it enables the kids to play with her while still being safe. Plus it will drain off some of that kitten energy and thoroughly tire her out before taking her break in solitude.
I think that ANY animal behavior expert would advise against too much unsupervised exposure between toddlers and ANY animal (much less a very young one). There’s just too much that can go wrong in a heartbeat without necessarily either kids or animal being at fault. It’s just not a good combination. Period.