I do not think one needs to travel abroad to see poverty. There is plenty here.
If you want your kids to realize how privileged they are, make them pay for some of the things themselves . You said they are swimming in cash.
Better yet, make them quiet the jobs they do not need, so some low income kid can get it instead and help her family pay the rent. Your kids can volunteer somewhere.
We have a much stronger social safety net, so I don't think there's nearly as much abject poverty in our country as in the US. Sure, there's poverty, but compared to what my daughter experienced in rural Myanmar it's on a completely different plane. Poor here includes universal medicare, universally available K-12 schooling, housing assistance, income assistance, the security of basic human rights, a transparent political system, freedom from armed conflict, and so on. I'm not trying to minimize the challenges of being a poor Canadian. But ... well, travel still puts a very different lens on our first-world privilege.
In our family we parents pay for basic clothing, food, shelter, and education (defined broadly, in the unschooling sense) from 0-18. But they pay for most of the discretionary things, beyond the basics. My eldest has paid all her college tuition so far with a combination of savings/investments, scholarships and employment income, and things are looking good for this upcoming year as well. We live simply and our kids are not showered with frivolous consumer goods. They haven't been given vehicles, or gaming systems, or cellphones, or computers. They've bought some of this stuff for themselves, typically after years of savings, but we're still a family without a lot of the typical "stuff." The kids are still video-game free and cellphone free, we're driving a 19-year-old minivan, have no Netflix, etc. etc..
My kids are flush with cash in that they currently have more income than they've ever had - because they have jobs that they applied for with good resumes and strong interview skills, and have worked hard at. This is a community with a lot of summer employment for teens and there are more jobs than kids to fill them. My kids are considered reliable good workers, so they have tended to be recruited by the more pro-active employers. But wow, I can't imagine encouraging them to quit their first jobs as some sort of life lesson. What kind of strange message would that send? How employable would they be in future if that was the upshot of their first job? Their employers would be angry, they would likely struggle to find replacement employees.
Do you really think that quitting a job is a good way for kids to appreciate their relative level of privilege in the world? Is throwing away one's privilege the only way to understand it? I'm willing to entertain that idea: that it is futile to try to understand privilege whilst one maintains it. But I'm not yet convinced that it really does the world much good on balance to throw away one's privileges. Ideally I'd like to find a way for my kids to gain enough understanding of privilege to want use their privilege for good, non-exploitatively, to try to make a better world.