There are no "weed" killers that are so selective that they would kill one broad leafed plant and not another. There are "weed" killers that will not adversly affect grasses but will kill broad leafed plants, but the glyphosate products are very broad spectrum and will kill any plant the product contacts.
Much better for you and your environment is the mechanically remove the weeds, or smother them with mulches.

As Kimmsr says, your best bet is to use mechanical control to take care of these weeds. I don't know of any weed killer that won't kill your trees, but then they are not a major tree so no weed killers will be registered for killing all but the trees. The Hollies also don't fall into a broadleaf category that I am familiar with where there are broadleaf herbicides that will kill broadleaf weeds but not the hollies, although there are a number of such herbicides for major agricultural crops.

Are you sure you got some glyphosate on the holly? Simply applying it near the plants won't hurt them unless you get it on growing parts of the plant. It may be they died from something else. If it was the glyphosate and you are spraying, consider using a glove or paintbrush or roller dipped in a concentrated solution that you can paint on the weeds to reduce the risk of drift or accidentally getting your spray on the holly foliage.

When you use a sprayer watch where the cloud goes. Even the best application will send up particles from where the spray hits. Most just look where the spray hits the plant they want to kill but do not look where the splash, if using coarse spray, or the cloud of fine particals. if using a fine spray, go.

The round-up can travel down the weed, leave the weed roots, travel through the earth, and be absorbed by the tree roots.