Hi! here's a few suggestions to control these plants: 

Curly dock is a perennial plant and mowing can definetly help delay seed production but mowing is not effective to kill the plant. As a mechanical control you may try and pull or dig the plant, making sure you get as much of the root as possible. If you already have some plants producing seeds you can cut the stalk and dispose of it away from the field to prevent further infestations.  Herbicides like Milestone are vey effective if applied to the spring or fall rosette (before it starts producing the long talk with the seeds). 2,4-D and dicamba mixes are also effective on small plants as well. 

Purple mustard: Same as curly dock, mowing can prevent seed formation, pulling or hoeing can also get rid of small plants. Chemicals like 2,4-D and dicamba are effective when the plant is small in late winter or early spring (before mid-April). 

The pesticides I mentioned here are usually safe for perennial grasses but may supress them for a while if you use high rates. These pesticide will often times be more effective if the plant is actively growing and not under any stress (do not mow or pull the plants before applying a herbicide). 

Always read the pesticide label!

-Karla Melgar Velis

Thank you very much for your information!