You have creeping charlie (Glechoma hederacea). It is one of the most vigorous and persistent of all broadleaf weeds. It is common in lawns and flower beds. It is difficult to control and almost impossible to eradicate. In the lawn, repeated applications of broadleaf herbicides, such as 2-4-D products will help slow it down, and hopefully keep it from spreading into the flower beds. Creeping charlie is resistant to many herbicides, so control will take time. In the flower beds, control is even more difficult. Herbicides here will kill the perennials you want to rescue from the green strangler. The best remedy is to weed and mulch, and weed some more, and mulch some more. Use a spade or a soil fork to dig deep to remove as many of the weed roots and runners as possible. Spot spraying with Roundup or a similar "kills-everything" herbicide may help, but be very very careful not to get the chemical or even of whiff of the spray mist on any of the flowers. Check with the Michigan extension service for more recommendations. The Master Gardener webpage (http://web1.msue.msu.edu/mastergardener) has links to lots of information.