Litter training troubles

Two weeks ago I adopted a pair of 5 week old kittens (yes, I know that's too young; there were exigent circumstances). At first litter training seemed to be going fine. I placed them in the box every thirty minutes to help them learn where the box was and how to use it, and they caught on quick. Because they were new and so little, I kept them in a single room of the flat, especially when I was gone to work or asleep, my very large spare bathroom. As they are now 7 weeks and older, I tried to expand their play area to my bedroom and the bathroom, which are connected. Everything was fine during the day, but then at night they went to the bathroom all over my bed. One of the babies was even soaked because he lay right back down on top where he peed on the blanket. During the next day when locked up they used the litter box fine again.

Could it be that terrible of separation anxiety that they won't even leave me to use the box? I know when I am with them they barely leave my side, even playing together on top of me. It's not an issue of not being able to find it, there's maybe a metre between my bed and the bathroom. I don't want to have to keep locking them up constantly, but I can't have them ruining my carpets and bed. Is there anything else I can do to help them? These are my first only kittens. In the past I have always had an older cat around to help out, so I'm not used to being momma cat myself!

Here are my angels. Sweet little American Curls.

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They are just little, and are having accidents. You'll need to put a small litter pan on your bed, and a few more around your flat, so they can always find one in a hurry. They will eventually grow out of this accident stage. Also put a big beach towel over your bed for now (just in case), and towels on the carpet. More litter pans is key here though!

 The advice  by sarthur2 above is what I would do too! Plenty of places to go potty, some towels just in case.

I think  the more in depth reason would be because they are so small, and young, the urge to go comes on quick and strong, so they can't be bothered to go search for a box if there isn't one not only in sight but close by. You could try putting an attracting spray in the litter boxes so they smell is from a bit further away and want to use it. 

 Good luck with those kittens they look adorable