Hey are you still having this problem?
This does not sound like a relay to me. This sounds like either an earthing fault, or a battery fault. I would do two quick checks to narrow this down a bit, mostly just because auto-electricians are freekin' expensive, but also because this could be a quick-fix.
1. Check the negative connection both at the battery and at the earthing stud on the chassis. If your battery is in the front this should just be a really short bit of cable [say 6 inches] from the -ve terminal of the battery to the earth stud, located near the right hand suspension mount. At the battery terminal, even if the connection feels secure, if there is some serious corrosion going on it will still destroy your connection. So if it looks like your battery has been snorting more white stuff than Whitney Houston [too soon?] I'd take the clamp off and clean up both the battery terminal and the clamp itself. Rough it up with some sandpaper or scour it with a screwdriver.
At the stud there should be a locking washer to help get a good connection. If not they cost like $0.50 at the Bolt Shop. Also rough up the surfaces to ensure a good connection.
While your at it put your multimeter on DC and test from the stud to the positive terminal just to confirm you have +12v. Whilst testing give the negative cable a vigorous wiggle and see if the voltage cuts out. Its unlikely but worth a try.
2. Take the battery out of the car and put it on a flat surface. Test to confirm you have +12v. Get some one to tilt the battery to either side while you continue to test for voltage. Do it both slowly and quickly to mimic turning in your car. If at any stage the voltage either drops below 12v or cuts out all together - you have your problem.
I know both of these are basic tests, but you'd be surprised at how often the fault is something really simple. Hope this helps.
