I fight this one as well as burdock. If you don't get them small, they get tall and woody and you have to use a reciprocating saw to cut and then smother them.
I keep forgetting that I own a weeding torch. Gotta be careful next year to not use it near my 30+ pine trees.
Curley dock is a tricky weed to eliminate. Getting it out of the pastures before it sets seed is key. I dig them out as soon as seen when they are small is easier than after the long tap root matures. Constant mowing will eventually get rid of them long term consistent maintenance. Every part of the plant is toxic to horses.
burdock is worse than curly dock IMO, but both of them don't seem to be spread by birds as much as perhaps other animals. we don't get them migrating into any of the more formal bare dirt gardens i use for growing beans, tomatoes and peppers.
i think i finally figured out where the speedwell in the onion patch came from, some old potting soil from a container was mixed in there last year...