Best way to rid garden of weeds that appeared since tree was removed?

Well now that the tree has been removed the area is probably getting more sun and the area has been disturbed bringing up weed seeds. I don't know if your ground cover is growing in this area--if not--you can spray with Round Up, wait a week or so and plant new ground cover.

Hello there, I was going to say the same as GK. Good luck!

Pull the weeds and put down Preen weed preventer. It will help by preventing the seeds from germinating. I agree that it is probably due to having a lot more sunlight now, so the hidden seeds are germinating.