We do not have an evidence that Zulaikha or her husband were Mushriks. Many scholars say that if the Azeez (King) of Egypt was a Mushrik, he would have never behaved with Yousuf in the way he behaved and he would have never given him the charge in the treasury of Egypt. Zulaikha tried to do wrong against Yousuf but she could not because of the firm faith and strong will power if Yousuf. Later in she has repented and become a good person. Allah (SWT) forgives every sincere person who repents and seeks forgiveness.
Prophet Yusuf (AS) was son of Prophet Jacob (AS). Prophet Yusuf became the leader of the country of Egypt when his father was not the leader of the country. The leadership of Yusuf over the country made his parents and brothers deal with him according to the norms of the country and society but that is a different matter from the status of the prophet hood.
Prophet Yaqoub (AS) was treating all his children equally but some of them felt jealous of Yousuf who appointed by Allah (SWT) as a Prophet. The fault was from those sons and never from Yaqoub who did not discriminate at all but was always just and kind to all of them.
The bad feelings and jealousy of these sons lead them to commit the crime which they committed against their own brother Yousuf.