Dollar weed is usually a sign of excessive moisture. Changing irrigation practices to allow the soil to dry out more in between watering will help. If there is a drainage problem that keeps the area too wet then that should be addressed too. Since dollar weed is a broadleaf plant it would be difficult to use a broadleaf weed killer in your broadleaf ornamentals without causing damage to them too. 

Glyphosate can be used for spot treatments around ornamental plants. Glyphosate is a non-selective herbicide that should be used with caution. Spray with a 3% Glyphosate solution in a pump-up sprayer for dollarweed control. Follow label directions for mixing and use. Do not allow glyphosate spray mist to contact ornamental foliage or stems, as severe injury will occur. A cardboard shield may be used to prevent glyphosate spray from drifting to nearby ornamentals.

Imazaquin (as in Image Nutsedge Killer) is a selective herbicide that can be applied safely around certain landscape plants; see product label for a listing of the tolerant plant materials. Imazaquin should not be applied around the root zones of plants that are not on the product label. It is best to apply imazaquin when weeds are small in spring. A second application can be applied six weeks later if necessary.

Glyphosate and imazaquin are both more effective when weeds are actively growing and may not work as well if applied under drought conditions. As with all pesticides, read and follow all label instructions and precautions.

Note, complete eradication of dollarweed (or any weed) from the landscape is not practical. Instead, a more realistic approach is to control (not eradicate) the weed by limiting the infestation to a tolerable level. 

Between hand pulling and reducing soil moisture you should be able to get it under control.