Is it permissible for a pregnant woman to pray to God to grant her what He sees as best for her and her husband in their religious and worldly affairs, whether it be a male or a female?

Delegating one's affairs to Allah and supplicating to Him to bestow upon you what is best for you is a commendable act, as is found in the Istikhara supplication. There is no objection for a Muslim to ask Allah the Almighty to grant him offspring of either gender (male or female) or both.