As long as Beth doesn't pass down her resentment and entitlement, her kid should be fine.

This. Obviously if Beth goes out of her way to be like "OMG YOUR STEP COUSIN GETS TO GO TO THIS AMAZING EXPENSIVE CAMP AND YOU HAVE TO GO TO THIS SHITTY LAME POOR PEOPLE CAMP" then yea, the kid is gonna feel upset that he didn't get to go to the better camp. But if she properly manages his expectations it won't be an issue.

I grew up pretty fkn poor. My parents could afford the absolute bare minimum essentials and that's it. I grew up watching other kids have nicer things, better experiences, more opportunities, all that stuff. But I never, at any point, felt entitled to have those things or felt that it was unfair that I didn't have them. I seriously don't remember ever having those feelings at all, even as a kid. From a very young age my parents taught me that Life Is Not Fair and sometimes other people have things we don't, and that's just the way it is. I was NEVER taught to expect to have the same things as anyone else and therefore it never occurred to me to be upset about it...