It won't necessarily work but you could try some scent introductions before your cats & your neighbours' kittens meet "in person". If you know your neighours well & if they wouldn't mind, perhaps you could swap some cat bedding with them. This way both the kittens & your cats can get used to each others' smell before any meeting. If you do this several over the next few weeks it may "soften the blow" when any face to face meetings take place. Similarly if you visit the kittens & handle them, & if your neighbour does the same with your cats, you can transfer the scent between your cats. It may just make the shock of finding new neighbours have moved in next door a bit less stressful for all the cats.
Female cats generally have smaller territory requirements than males plus they can learn to time share overlapping territories. When your neighbour first decides to let her cats out, ask her to let you know so that you can keep your cats indoors. That way the kittens can explore & leave their scent around her garden, plus pick up your cats' smells, then the scents of all the cats starts to mingle & become one communal scent. Also your cats are likely to know the sex & age (as in they are only kittens, not sexually mature adults) of the kittens & not be so worried.
This may help with the introductions & smooth the path to amicable sharing arrangements. This is what I did when my neighbour got a kitten & I had 4 large male cats. It worked really well & the neighbour's kitten ended up running rings round my 4 who got hours of entertainment watching the kitten catching butterflies

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