If you are trying to kill grassy weeds, a grass-selective herbicide can be used to kill only grasses, leaving broadleaf plants (like your dogwood) alone.  More information on products and application methods can be found here: https://yardandgarden.extension.iastate.edu/how-to/how-manage-perennial-grassy-weeds-garden-and-lawn

If the weeds are a variety of broadleaf weeds, then there is no selective herbicide that can be used that will kill those weeds and not potentially damage the dogwood plants.  You can target your applications only to the plants you wish to kill being careful not to come in contact with green tissue on the dogwood plants.  A non-selective herbicide (like glyphosate) or a broadleaf herbicide (like triclopyr or dicamba) could be used - as long as you are very careful about how it is applied.  More information here: https://yardandgarden.extension.iastate.edu/how-to/how-manage-perennial-broadleaf-weeds-garden-and-lawn

If you are unsure what type of weeds you have, more information can be found here: https://yardandgarden.extension.iastate.edu/how-to/types-weeds-landscapes-gardens-and-lawns