I will be in Canada for a month or so visiting family
My original plan was to get my licence in Canada and then convert it, but I have been told numerously that doing it in 4-5 weeks is not likely,
The two quotes taken in combination is the problem.
You can get a PPL in three weeks even. I did it in Florida a while back. (See the sticky elsewhere in this forum.) But here's the catch: It requires total dedication.
I spent several months ahead of time studying all the theory, 2-3 hours an evening, three evenings a week. And while I was in Florida I was flying, or doing things related to flying, seven days a week for 21 days straight. Yes, initially each flight is only an hour but expect half an hour before and afterwards with the instructor briefing, plus two hours digesting the flight and preparing for the next one. So those two flight hours all of a sudden translated into eight hours. Then you've got to pass the theory exams: Under EASA that's seven exams that take at least an hour each just to sit. If you need any preparations, or a retake, expect even more time.
And then by the time you get to go cross-country, the flights get longer but so does the preparation work.
I'm not trying to discourage you. In fact, I found the experience of immersing yourself in aviation for three weeks, and coming out of it with a fresh license, immensely rewarding. But do take it seriously. Don't expect this to be a holiday with a bit of flying on the side. Don't expect to see much (or anything) of your family. And do expect a lot of theory study and other groundwork before you leave.