If you have the money and want to learn quickly then take a course or hire a professional to teach you a specific skill set. Then take those skills and use them in the mountains with clubs like ACC or BCMC, or with friends. For example, sounds like you have experience in the basics of backpacking and navigation, so you could consider hiring someone to teach you rope systems, crevasse rescue, and glacier travel.
If you are wanting to do actual mountaineering, you generally won't be allowed to join the club trips without prior experience. They will often do screening. Eagerness to learn isn't usually a qualification on trips where there is potential for injury or death. While I've learned a lot from trip leaders in the past, they are not guides or teachers, and shouldn't be treated as such. So, where do you get the experience? My guess is you and your wife don't have a lot of mountaineering friends, or you wouldn't be asking strangers. Best option then is to learn from the pros.
Agreed that the courses run by BCMC and ACC (still under $300 bucks?) are a great place to start (I took one years ago), but because they are short, they are not very thorough. I could be wrong, but I don't think the leaders (though knowledgeable) are certified guides or instructors. Great place to meet other like minded people though and build some contacts.