It's really hard to advise on this and it may be time to talk to a qualified behaviourist. And as Trini said, pain can account for all sorts of unusual behaviours so it may be time for a vet check.
I think the mat has to go though. It's probably become a cycle now that needs to be broken. I wouldn't put anything down in that area at all - you don't want him rehearsing the behaviour with something else.
Hard to say if there is any separation anxiety - is he exhibiting any other behaviours that make you think that? Try leaving him with a Kong or some other treat dispenser when you go out. In addition to helping if there is any separation issues, it might also break any habits of peeing while you are out. Give it to him on his bed so it increases the value of his bed.
Is it possible to separate him and Darla? Maybe take him for separate walks a couple of times a week to boost his confidence. If it's too cold for separate walks try individual play times - but keep him occupied with a Kong when it's Darla's turn so he doesn't get jealous. Might also be worth 'zoning' so each dog has an area that is their own (esp for sleeping and eating).
Years ago, when my two were very young I had issues with Deska bullying Tully (and Tully was head-strong). I saw a vet behaviourist about it and she suggested separating them when I wasn't around by putting up a baby gate. That way they could see each other but had their own spaces. They were also getting one walk a day individually and when I was home they had to stay on their mats/xpen at different sides of the room. I used the x-pen to make a barrier between rooms and after a couple of weeks Deska started springing Tully out so I figured he wanted her company, and they were fine after that. I think Deska just needed some space and also time to realise he did like Tully. Maybe your two need time apart for Hugo to realise he does want to share with Darla.
