I agree about the sweet william. I have both plants in my yard. If you planted only one coneflower, while it does spread it wouldn't spread that rapidly in one year.At least that has been my experience, at least here in New England.Thats a pretty established group you have there, its possible that those were planted a long time ago and have been lurking underground and this year they came up. Maybe when your Mom planted the Coneflower it stirred something up.I have had that happen with my poppies. I planted them years ago and they never came back and then suddenly after quite a few years a whole group of them appeared in the very same spot I had planted them years before.
The group you have there are very pretty.
I agree with Pat, try looking in the group for your coneflower and replant it somewhere in a space of its own.