Grrr, what! Can`t see what the problem is! I know he is a relative but I have to say it. Stupid man!!!
Ok, straw or hay may work, the only thing is, your dogs are Goldens, right, with the long hair? If so they may get a lot of it stuck on them and could be a devil to groom out. Though even that could be better than the mud I guess.
Trying to think of something positive you can do... and I am not doing very well! Let`s see, I guess it all depends on the size of the muddy place and what you can afford and I don`t know about the price of the different stuff over there. Ok, first thought, after permanent paving, would be the most expensive, some black ground cover stuff (made of a plastic type material but porous) covered by pebbles/gravel something like that. Second thought is tree bark or coco shell, coco shell is better because it sort of sticks together. I have the bark, it is messy when the dog runs all over it but better than mud!...(You know I am convincing myself here not to go for replacing with grass come spring after all but to go for the pebbles! Won`t need mowing.)
Anyway, sorry I couldn`t come up with something better. Best of luck with whatever you do.