According to this article, Eastern rite Catholics in North America have been able to ordain married men as priests since late 2014:
Apparently it was originally forbidden in 1890 because the Church thought the average Catholic wouldn’t be able to understand why some priests were married and some weren’t able to marry. Now it looks like that rule was repealed in 2014. The bishops of W. Canada recently visited the Pope, including a Ukrainian rite bishop, and they discussed married priests. It didn’t seem to be a problem. So why are the bishops of the Byzantine rite not going along? Are the Eastern rites so different that you couldn’t simply go to one of the other rites who are willing to ordain married men and get ordained there?
I was researching a totally different topic and came across this article: tabletmag.com/jewish-life-and-religion/94336/prelude-and-fugue
It concerns a woman living in Israel who was going to get married to a Jewish man who was very secular. All of a sudden he became very religious, and she didn’t fit into the picture and he broke up with her. This is her view of the situation. She is now the music critic for the NY Times, by the way. In reading some other articles about Eastern rite priests, it was very clear that the wife must also feel a vocation and be in complete agreement with her husband’s desire to become a priest. I personally feel your primary responsibility is to your wife and her happiness. Good luck.