after the death of the jp parent

I am living in japan and I was wondering what would happen to my children if at any time in life my japanese husband passes away?
can i take them and move to my country or the law give the right to the japanese grand mother to take them fom me?
and do i have to get some approval from her or something?
or is there a vise which can make me stay with them in japan and raise them up?

No lawyer here, but this is what I know:

Have the children been registered in Japan, meaning they have Japanese nationality? If yes, then they can stay, and if they are still young and need parental care, you can apply for a change to long-term visa and stay in order to raise them.

If you want to move to another country with the children, that should be no problem too. The law does not give the right to the Japanese grandmother/relative to take them away from you.

You can stay here as the mother of a Japanese national.

Work on getting Permanent Resident status and you can stay here if your husband dies, or if you divorce.

Sorry if this is unnecessary comment.
About inheritance:
If you and children have been registered in family registration, called koseki, with your husband, you and children would inherit property from your husband (even if you and children have not Japanese nationality). In this case the grandmother has no right.

Rule of thumb for unpredictable is to have the insurance from. Especially in Japan, whereas having a grandson that will continue to uphold the family name. Although unlikely the grandparent will attempt to impede and meddle against your right to sole custody of your children, nonetheless having a written document will ensure your husband wish for you to have a sole parental right will be honored by the Japan Family Court. Talk to your husband and have him confer with an attorney. Additionally secure your children your national citizenship and their passport… Assert yourself.