Help please. 14 week old kitten peeing everywhere in my house

So we got a kitten a few weeks ago. He has been peeing in the house since we got him. At first I thought oh okay maybe it’s just an accident, new big house, he’s still little etc, but he has been doing it so much Im starting to not think so anymore. He’s peed on my kids beds more than once, I have had to do multipllle loads of “pee” laundry , went through 2 bottles of stain remover. I just now caught him peeing in my sons stuffy bin and when I emptied it I found another stain on the bottom so I know he’s done it twice, now ill probably have to throw out half his collection:( He isn’t fixed but the vet said they won’t do it until he turns 6 months . I do have another cat but we have 4 litter boxes , spaced out, I even brought one of them away to it’s own space at the top of the stairs.

He does use the box, and half the time when I catch him and run him to it he finishes peeing, so why is he also peeing all over the house? Shouldn’t he know by now that’s where he goes? I’m starting to get at my witts end and I would absolutely hate to have to rehome him because other then that he’s so sweet and a perfect addition to my family, so we really need to correct this:( we keep the doors to the rooms closed now but if one of my kids forgets or its open for a small amount of time 90% of the time he goes in and pees somewhere