Your wife is right. I would always have an excuse why vacationing with 4 kids was too expensive, and I would rather be spending $10K or $12K on another upgrade to our house versus spending it on a Beaches vacation in the Caribbean. And I would get bored renting houses at the East Coast beaches that lacked the amenities or atmosphere I wanted, or required us to always travel with 3-4 other families because the weekly rental was $4K-$8K during prime season.
My wife is the one that finally pushed us into timeshares. So I am relatively new...and late...to timesharing. Now I wish I had bought our first timeshare years ago. Some of these long timers here on TUG bought timeshares in HHI or Myrtle Beach back when they were being built or fairly new, so they raised their families going there once or twice a year and have many years of great vacation memories. We have some of those memories, but not enough. If we had owned a timeshare earlier (the right timeshare for us) it would have forced us to take many vacations I postponed due to work, home projects, whatever.
You are already ahead of the game buying resale. Just buy something at a fair price (on the resale market) that will always retain some value (if even if that value is $1). In my opinion (hypothetically) you would be better off spending $10K-$20K on a prime summer week (or prime winter week if you are a skiing family) that you know you can use every year versus spending $500 on an off season week thinking you can depend on trades to get where you want to go. I don't own in any points systems, which sound like they may have some value to you, so others here are your go to resources for those points questions.
There is a rule I have learned to be true and firmly believe in. I just wish I learned it years ago. Own at least 1 week per year (deeded or points) within driving distance of your home during prime vacation season (prime winter or prime summer) when you can take your entire family there. The term "driving distance" varies by individual as for some that means 3 hours, others are okay with 12 hours. But being able to take your family to a place you can drive to, when they are off school, and you don't need to worry about the expense of plane tickets and schedules for 4-6 people, makes it more likely you will take at least 1 quality vacation a year with your entire family to your "home" resort.
Everybody loves the concept of Mexico, Caribbean, Hawaii, Europe, Asia, etc...and for sure those trips will happen. But a simple vacation that doesn't require complex planning at a nearby family favorite resort is proving to be invaluable to us. It has worked out so well for us, we have family members that are now purchasing their first timeshares during the same week and same resort we own at.
Best wishes on your decision.