Is it permissible for a widow with children to remarry and keep her children?

A woman can marry after her waiting period (iddah) ends. The waiting period for a widow is the delivery of her child if she is pregnant, or four months and ten days if she is not pregnant. As for her right to custody (hadhanah), it is prioritized as long as she does not remarry. If she remarries and someone with the right to custody disputes her, custody transfers to that person. If the person who has custody waives it, the right transfers to the next eligible person.