Argh! Cannot get dogs to quit peeing on bed...

A year ago, I posted a humorous incident of discovering my newly adopted puppy had peed on my bed. One year and several midhaps later, it isn't very funny anymore!! Please help me, somebody!

I have two adopted toy poodle boys, both neutered, now 16 months old. They were rescues from a puppy mill, and the adoption shelter pad trained them. We started potty training outside when they came to us, but never quite got to good! They don't soil their cage and they don't go on the hard wood or laminate, but continue to think soft spot = toilet. We have had a dog gate up to keep them out of the rooms with carpet since that's where they like to go. It has been up for about the last 8-10 months, and if they ever manage to sneek through, they'll usually go and potty on the carpet. We are moving soon, and I'd really like to get them trained so I can trust them on carpet in our new house.

One of them (cooper) had occipito-axial instability and had to have spinal fusion surgery after which he was on cage rest for about 3 months. His only time outside was to potty, on a leash, and he got pretty good during that time. Now, he has recovered, and rarely has mishaps, although he still sometimes pees on our other (big) dog's bed, or poops on the carpet (less than once a month).

the other one (guy) has the horrible habit of peeing on our bed. It's very strange since he sometimes gets to sleep there with us and loves that - he makes little nests of our duvet - and I don't understand why he would want to go in his bed... I don't think it's a dominance thing - he's very shy and timid, follows commands well and generally acts very submissive. As a result, we can't ever leave them unsupervised in our bedroom (one of two rooms that don't have carpet) meaning they only ever get to be out in the kitchen.

I feel like at this age, they are not going to get better without me doing something proactive, but what? When we are at home, they get to go out at least every 4 hours, they manage great overnight in their kennel for 8 - 10 hours (sleeping in on weekends) without soiling or whining, so I know it's not a physiological need when they pee on my bed 90 minutes after having been outside.

Please help!