Her husband's stepfather's account is in Hong Kong, and her mother-in-law's account is still in the Mainland. Can my husband apply for a Hong Kong account?

I can't. Not to mention Hong Kong nationality, even if the mainland provinces transfer their hukou, only your mother-in-law can transfer the hukou to her husband's name. As for your husband, if he is a minor, he can move with his mother, or apply for asylum for his parents and children in the future. Now that he is married, he is at least an adult. Sorry, I don't accept such asylum.