Thank you Torontosm and Rob_TO, your advice has been truly helpful.
Just to share my findings, I also found that there's an option of coming to Canada as an international student. If my wife got accepted to a university, I and my kids could accompany her and stay in Canada for the duration of her course. During this time, my children can attend public school free and I will be granted a work permit so I can support her financially. This will allow me to gain Canadian work experience through which I can apply for a PR, especially if I get a full-time job offer.
My wife would also score half-days for each day she spends in Canada for the duration of her degree. After graduation, she can apply for a work permit herself and get a job, which would also add to her ability to qualify for a PR.
I figure, worse case scenario and nothing else works out, this would be a good option for both of us.