You'll actually find that's common all over Europe. Not always, but there are a lot of hotels that will only allow two adults in one room. You either have to book a triple or a suite, which not all hotels have, or book two rooms.
Last year I traveled by myself, but I had my two older teenage grandkids with me. I had to book a triple room at both of the hotels we stayed at in London and Paris.
How old is your teenage son? There are some hotels that will allow a cot in the room for a child, but there's an age limit on that ( (usually around 15 or 16). If he's older than that, you're going to be stuck either getting two rooms or a suite. Edit: Sorry, I just saw the last line where you said the one hotel only allows children under 13. Yeah, that's lower than many, but again that is relatively common throughout Europe.
Just out of curiosity, have you thought about staying in Alesund instead? Is there a reason you're staying in Geiranger? It's a pretty small place, and if you wanted to see it, you could easily visit from Alesund.