Is it a proper landscaped rockery, or just a pile of rocks dumped higgledy-piggledy, plum pudding style?
Do you want to keep it as a rockery, or would you be happy to eliminate it and use it as, perhaps, a shrubbery, or for veg? Have a good think about how you want it to look in the end, without being ruled by what was somebody else's vision many moons ago.
I'm going to say what I think you probably don't want to hear. You can
never get rid of couch and brambles from a pile of stones, or a properly designed rock garden either. It becomes a never-ending war, the garden never looks right, and you will never be satisfied with it.
My suggestion is that this winter you dig out any plants you want to keep, make sure there are no perennial roots tangled with theirs, and plant them out somewhere else, or pot them up in buckets to put back once the work is done. Then, dismantle the whole pile, remove it, dump it on the furthest bit of your land, or use it to reinforce a path, or whatever.
Then you have a flat piece of land, in the sunniest part of the garden, which is a blank canvas.
How about making an area where you can sit out for a coffee, lunch or to entertain friends? Surround it with a couple of large beds filled with low maintenance perennials and ground cover, lovely scented flowers and so on, maybe climbers up an arch. Suddenly your eyesore has become a lovely feature.
If you can use machinery to help you clear away what was there before, then it could be done in just a few days of hard work, but it would absolutely be worth the effort.