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I'd not heard of 'sizing' or lining paper until it all started to go wrong honestly.
The instructions that came with the wallpaper mention sealing a wall if pourous, but I thought it would be ok with two coats of white paint to onto. How necessary is the lining paper?
ILb-
Lining paper helps to cover a lot of problems. If you're using an expensive wall paper it's advisable to line the wall with a lining paper running at 90 degrees to the wall paper. I usually line walls and paint on top.
Where I've seen the problem you're having is when the ceiling has been painted and few inches of the wall below it (or the cornice). When you apply the size to the walls the fresh emulsion paint gets mixed up with it. It doesn't usually cause a problem bleeding through the lining because it's more often than not white.
Paper hanging is way more complex than anybody thinks until they try it. I consider myself fairly experienced with lining paper but I don't hang wall paper professionally. Last year I had a nightmare with some thin lining paper and only just pulled my ass out of the fire.
Airhead
Have a look at Gardz, I'm not sure if it's designed to do what you want but it's similar.
Double lining is an option but you don't mention what type/weight of lining paper you're using.
As already mentioned the walls should be 'sized'. In this day and age that's normally with the same paste as you're using for the paper. There are a couple of different types of paste but I usually use it premixed and I don't dilute it for sizing.
It seems from your description that the paint didn't have enough time to dry properly, I've seen this happening with papering before, normally it's a light colour and doesn't permeate the paper. I always use a thick lining paper these days, the lighter stuff isn't worth the problems it can give you.