With small children, LVT vinyl is definitely the smartest choice, in my opinion. Humidity isn't even the main issue - the real advantage is that it holds up incredibly well to impacts, dropped objects, and stains. Laminate, even good quality stuff, scratches easily and if water gets spilled on it (and that happens constantly with kids) it risks swelling. In my case, I went with LVT in my kitchen for exactly this reason, and after years of real wear - toys thrown around, broken glasses, everything - it still looks brand new. Cleaning is minimal, just a mop and you're done.
The higher initial cost of vinyl pays for itself because it lasts twice as long, maybe three times longer than laminate, especially if you have little ones running around. Brands like Tarkett or Gerflor are reliable, they have decent thicknesses (at least 3-4 mm) and warranties that actually hold up. Another thing: vinyl feels warmer to the touch than laminate, so if your kids walk barefoot it's more comfortable. Sure, it costs a bit more, but it's an investment that makes sense when your home needs to take a beating.
The only thing to check carefully is installation - the subfloor needs to be perfectly level and dry, otherwise the vinyl can ripple. If you have someone who knows what they're doing install it, you won't have any problems.