Ok, so let’s look at the scenery from a somewhat neutral perspective:
In your house, there’s not just one other cat, there are actually six others competing for resources. That’s a lot of potential conflict and you observed that your cat is staying away a lot more since the arrival of the kittens.
On the other hand, at the neighbor’s home, a territory became vacant when the previous cat died. No competition, peace and quiet and - reading between the lines - food and cuddles also freely available.
For a cat, it’s perfectly logical to wander towards the neighbors’, either as second home or even permanently. At ten months, looking for an own territory is normal.
To be blunt, cats on average are not loyal to people in the way dogs are. If they find a more appealing home, they will move (if the humans involved let them).
You should first talk to your neighbor. If your kitty isn’t permitted in at their house, that’s an important step. You may have to get creative, especially as your cat is possibly filling an emotional void due to the traumatic death of their cat.
Second, make sure she’s comfortable at your place - especially that she can have peace and quiet if she wants to sleep and that there’s no rivalry between her and the other cat. It’s possible that the new mom has become more territorial with the arrival of the kittens. My gut feeling would be to very carefully watch the situation at your home, conflicts can be very subtle, not always fur-flying and obvious fighting.
Apart from not permitting your cat to go outside, there’s not much you can do to be sure she won’t move out, especially if the main cause is discomfort at home and not the lure of the neighbors’.