All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It was authentically reported in the hadeeth of the Prophet that it is forbidden for the wife to request a divorce except for a legitimate reason. We have previously underlined those reasons in fatwa 131953. If your husband is having an affair with this woman and he insists upon it, then this is sufficient reason for requesting a divorce because his conduct is impious and dissolute.
A written divorce is considered a metaphor of divorce on account of which divorce takes place if the husband intended it. Please refer to fatwa 174947. If your husband intended issuing the divorce while writing the words of divorce, it counts as a divorce and you are obliged to observe the ʻIddah. It is impermissible for you to go out except for a need. If there is a need, you go out for it during the daytime or, if necessary, at night, but you return to your house to sleep there overnight.
It is obligatory on the husband to provide for his divorced wife during her ʻIddah until it expires. If your husband does not provide for you and you need to go out to earn a living, then there is no harm in that. The same applies to visiting the doctor.
As for going out to take a class in college, then if getting a job depends on taking this class, it is considered a need and you may go out for it. However, if this class only helps you get a better job, then, apparently, it is not a need.
It is impermissible for you to leave the house during the ʻIddah to celebrate Thanksgiving with your family. It is impermissible for the Muslim in general to partake in the celebration of non-Muslim festivals. It is also impermissible for you to leave the house merely to exercise for fitness, as this is not considered a need that allows going out during ‘Iddah.
Finally, Islam commands the husband to live with his wife in kindness. Allah, the Exalted, says (what means): {...and live with them in kindness...} [Quran 4:19] As-Saʻdi commented on the verse, saying, "It is incumbent on the husband to live with his wife in kindness, keep good company with her, avoid harming her, and treat her with compassion and respect." There is no doubt that a strong temper in dealing with the wife, neglect, and disrespect contradict the enjoined kindness and good companionship.
Allah knows best.