I think you will find that most airlines require the "unlimited right to live and work in the European Union". A residence/work permit on the grounds of family reunification does not count for multiple reasons: 1) your right to live and work is tied to the country in which your spouse resides. Now as an EU citizen, s/he can live and work in any EU/EEA country (also CH), but that is where your right to live and work will also be. 2) Initially, under family reunification rules, you will only be given a temporary right to live and work in that country, thus it is not "unlimited". Your residence permit does not become permanent under EU family reunification until five years of continuous residence or you meet the requirements for citizenship in the country in which you reside. That can be as little as three years for some EU/EEA nations. But basically, it will take at least three years of continuous residence in one country before you can get citizenship and thus "unlimited" right to live and work anywhere in the EU/EEA/CH.
That being said, it would be worth looking at your ancestry, particularly if you are from South America. Many European nations have expedited citizenship pathways if you have ancestry from that country. Spain and Portugal specifically have some expedited procedures for people from most South American countries. If you happen to have Irish ancestry no further back that grandparents, then you either can claim Irish citizenship, or already are an Irish citizen. In some cases you can go back as far as great grandparents.
Anyway, I would not count on a job in Europe until you actually have citizenship yourself. Occasionally you may luck into one that just requires the right to live and work in one country, but it is pretty rare. But look at every country and see whether you can claim citizenship based on your nationality, or see which countries offer the quickest path to citizenship and see if you can establish yourself there officially and then commute for a few years.
As for the EASA exams - You can do the 14 theory exams through any EASA member country, but all 14 have to be done through the same country. You cannot do 7 in the UK and 7 in Ireland. Your license will be issued through the country that you get your initial EASA medical exam through. I think every EASA member country requires the initial be done in-house at their national aviation medial center(s). After that they can be done anywhere. As mentioned, the UK conducts theory exams in the States (Orlando - just down the street from Universal Studios), and I believe there are a few UK approved medical examiners in the States as well that could do renewal medical exams. Also your skills test (check ride) can be done using examiners from any EASA member country, so long as approval is granted ahead of time. For myself, I did the theory exams through the UK, the medical and license issue through Denmark, and a German examiner did the skills test. It took me about nine months from when I initially started studying earnestly to having the license in hand.