I shy away from chemicals, usually, but maybe if you used a broad-leafed weed-killer on the grass, it couldn't invade your flower beds from the lawn, and vigilant hand-pulling might work in the garden.

I've found that Brush-B-Gone works on ground ivy without killing the grass - although your grass may turn somewhat yellow for a while.

Further, fertilizer with boron in it helps to control the stuff.

Pulling is great therapy.

Using all three methods, I've managed to get the beast under control in an area that was once almost total ground ivy.

Unfortunately, I'm beginning to find it in areas in my field and in the woodlands. The woodlands stuff is easy to pull; the field ground ivy gets a dose of BBG.

P.S. BBG also works well on garlic mustard.