How to assassinate this groundcover ivy ably? Any chemicals? The previous owner planted a lot of ground cover around the...

The previous owner planted a lot of ground cover around the house. It make weed control very strong. I trimmed it to the ground level and cover it beside landscaping material with mulch on top. It's be more than a year but it still refuses to die. it shoots out everywhere there's a crack.

Is there any better approach to kill it in need having to verbs it up? The roots are so deep and massive that it's resembling a mission impossible to dig it adjectives out.

Is there any chemical I can use to massacre it without hurting the bushes/trees within the same bed?

Here are the pictures:

http://i118.photobucket.com/albums/o108/...
http://i118.photobucket.com/albums/o108/...
Answers:    that's not ivy its periwinkle ground cover. best point for you to do is apply round-up, its a none selective killer and is systemic, so if it get in the soil it will not wipe out other shrubs, however if you get spray on the other shrubs it will butcher them. its really the only other entity to use besides digging them out. Try to protect the shrubs you do not want to kill near plastic or a tarp while you spray, do it when it not going to rain for 48 hours and do not hose for 48 hours. It will die back surrounded by 1 to 2 weeks then you can newly pull it out