Is it permissible for me to promise a girl to marry her as a second wife after first satisfying my parents by marrying a virgin girl, knowing that the girl is divorced and older than me, and my parents reject her?

There is no harm in promising a girl marriage as a second wife after marrying another. The promise must be fulfilled if she agrees. Marrying a second wife is permissible for one who can be just. If the divorced woman is pleasing in her religion and character, her family should not prevent marriage to her merely because she is divorced.