Greetings Dave,
Seeing that you already plan to use Round Up around the trees anyway, go ahead and carefully apply Round Up to kill the grasses as well. You can use a sheet metal cone or a plastic cone to cover the seedlings and apply the herbicide around the perimeter of the tree ground line (making sure not to drip herbicide on the trees after removing the sheet metal or plastic cone).
No sense buying a different herbicide when Round Up is an excellent grass herbicide :-) Make sure to read the label and be careful!