Why would a sunscreen leave streaks and handmarks (This is on many different brands)?

I’m scared to use sunscreen anymore because of the dubious results I have had in the past. I personally slathered a new bottle of the stuff on my kids, made them wait until it was dry (according to directions), and only sent them out to play. When they came in after an hour or two in the sun they had red streaks and one even had a hand print on her skin! It freaked me out. At first I thought it was a freak accident. So I bought a new bottle, and this time dumped it all out and stirred it all up before applying. I had similar results. Another time two of my kids went on a trip to Ecuador. They used SPF 50 and it was as if they didn’t use sunscreen at all! They nearly had to be hospitalized from the burn they received. I’ve called different manufacturers and asked them about this. They did not believe me, but it happened. Are we just freaks of nature?