Hi, 

You can view our page on wild onions and garlic to reference maintenance. There are herbicides listed on there. You can look for products with the following active ingredients: 2, 4-D, MCPP (mecoprop), Dicamba*, or Triclopyr. or a selective herbicide. These will kill the onions/garlic with out harming the grass. Don't use anything with Dicamba over tree roots as it will harm the trees. Maybe you can just hand dig in those areas. 

Make sure to read label directions on anything you choose to use. Since you have a large area you may want to invest in a backpack sprayer if you don't have one, as you may need to reapply or apply again next year. Only mix the amount you need when you spray as it can go bad once mixed. 

You can practice some healthy lawn tips to help deter weeds like wild onions by aerating and overseeding with a preferred seed mix in the fall. 

Let us know if you would like to point you to more of our lawn care pages for proper care and maintenance. 

Emily