
I sympathise with your problem, but the first idea to put right out of your head is that Taffy is doing it 'to get Dougal into trouble'. Taffy may be doing it, but he will not be doing it for so complex a reason as to get the other dog into trouble! Dogs simply don't think like that. To find out for certain which dog is wetting at night I would suggest you crate them separately at night - the one with the dry bed will be the innocent party!
I'm no expert, but I would hazard a guess that Taffy is still unsettled about having another dog in the household, and is trying to make sure the 'interloper' (in his eyes) knows that he (Taffy) has a right to be there too. He is marking the favoured territory as being his. It can take some weeks after castration for a dog to stop smelling 'male', and maybe when this has happened with your new dog Taffy won't feel the need to stake his claim so much.
The easiest way to prevent this happening is to deny both dogs access to your bedroom. However many people like to have their dogs in their room, so maybe you won't want to do that. Is there are particular area of your room where he cocks his leg? If so then make sure you clean the area very well with a solution of biological washing powder and a wipedown with surgical spirit to remove any lingering scent (that the dog can still smell, even though we can't) that is encouraging him to use the same place. Don't use anything containing ammonia because this will only encourage repetition.
Hope this helps.
:)