Hi, Mandy. First of all, thank you for your active interest in your fiance's military career. There are a lot of military spouses who don't care and/or can't understand. (This makes it very hard for the service member, his/her family, and ultimately the Army.)
Secondly: I am an Infantry Officer. I have recently worked in the Infantry School. I think I can tell you some things about your fiance's situation. Caveat: I am a single guy, so I have never personally dealt with the family side of things (although I know many people who have). Also, I am not a clerk. So there will be many details of the financial side that I cannot answer.
Okay, then. Third. This is how it worked when I finished my Basic Training in St-Jean, and rolled out to Gagetown: It was about 50/50% of the guys who moved their spouses out to NB. Depending on how long they anticipated their next course to be, and what their perspective hopes for the future were, they had to make that decision.
As you have noticed, there will be different situations your fiance will find himself in: (a) on course, (b) awaiting training, (c) trained. Let me write about those in more detail.
When your finace is on course (a), specifically, on CAP/BMOQ-L he will be "ordered into shacks." This means that he will be required to stay in the barracks with his peers. I think it's bunk beds now, six or eight to a room. And the instructors will check, and they will find out if he has been living there. This is because his Section will be working late into the night, and they will need his participation. That said, as above, many guys still decided to move their spouses out to NB. I cannot comment on the financial implications of that, other than -- a military house in Gagetown costs about $450-550 in rent. The insulation is very bad, so in the winter the heating bills are very high... Anyway, your fiance MIGHT be working until very early in the morning until very late at night. He might also be working weekends. So, despite that fact that you are geographically close, you might not see him often.
The next point, (b) if your fiance is awaiting training... I do not know how the Engineers run their PAT (Personnel Awaiting Training) Platoon. In the Infantry School, they report to their supervisor only twice per day (last I checked), and in the interim they just do whatever. They do not have to live in the barracks. Sometimes, however, we try to "task them out": to send them on jobs that will increase their skills/knowledge. As an example, when I was awaiting training between my courses, I went to Ontario for 6 months to teach young soldiers. This was purely voluntary, however. I could have remained in Gagetown, playing computer games and drinking beer if I wanted.
Finally, (c) once your fiance is fully-trained (as I understand it, Engineer Officer training takes a long time, i.e. measured in years) the unit to which he is posted (this could be many places in the country) will help with his move out there. Again, I don't know financially, how this might work for you. If the Engineers are like the Infantry (for Officers), you will be moving back-and-forth to various locations every 2-3 years. Such is our life.
In closing, again, thanks for your interest. As previous posters have said, it's a hard life but seldom boring. Good luck!