A kind of Convolvulus, most likely C.arvensis.

No herbicide that will control this weed can be used over your desirable shrubs without harming them. You will need to isolate the weed in some way, either by careful spot spraying or wiping of a herbicide, so you can just apply to the weed foliage to control it. It has extensive underground root reserves, and will need followup control no matter the technique.

When I encounter weeds like this, I try to detangle them from the plants I want to keep. Then I can lay a few sheets of newspaper on the ground, spead the weeds out on this and spray safely away from other plants.