Does the mother of my four daughters lose her right to their custody by marrying a man who is a stranger to my mother (the daughters' mother)?

The custodian's right to custody is forfeited if she marries a foreigner (non-mahram) to the child, whether she is the mother, grandmother, or another relative, due to her preoccupation with her husband's rights over the child's welfare.

Therefore, if your daughters' grandmother (their mother's mother) marries, her right to custody is forfeited and transfers to the female who is most deserving of it. It does not transfer to you unless there is no one more deserving of it than you.

If the mother's or grandmother's custody becomes void, it then transfers to the closest female relatives of the child, in order of proximity, and then transfers to the father if there are no women more deserving than him.