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Don't worry this will not kill your new shrubs or trees. It is a systemic residual weedkiller. This weed killer will stop weed seedlings germinating in the ground(residual)and kill any weeds that have been sprayed through the leaves(systemic). As long as the gardener did not catch the leaves of your new plants all will be fine.

You just have to pick a spot and get after them. I love my Stirrup Hoe for things like this. Here is a link to one for you: http://www.acehardware.com/product/index.jsp?productId=1334167 With these hoes you can rake them back and forth and cut those nasty weeds off just below the ground surface, then use a little rake to gather them all up and get rid of them. The weeds that are too close to the desired plants can be hand pulled. The time and sweat poured into our gardens will yield great rewards!

Follow all mixing and application directions on the packaging.
Never mix different chemicals unless directed to do so by the manufacturers directions.

The process is called Phytoremediation.
These links have more information.

http://www.ars.usda.gov/is/pr/2007/070123.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/contaminated-soil-treatment.htm

Woodland or Wild Violets can be difficult to control ( I am having an issue with these in my own flower beds!)
Here is a link that may have some help.

https://www.gardeningknowhow.com/ornamental/flowers/violet/kill-wild-violets.htm

You shouldn't need to drill holes in your concrete. This article provides several methods of killing unwanted trees (without ruining your concrete):

https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-kill-a-tree-killing-trees-in-your-garden.htm