The main advantage of the variable filter is that you can turn it so that it is at the minimum setting (letting the most light through). At that point it's about the same as having a normal polarizing filter, so should be easy to focus. Once focused, then carefully adjust the filter to darken to the desired density.

In order to get long exposures in the daytime, you are probably using the filter near maximum density and also lowering your aperture to f/22 or smaller. If so, your lack of focus is most likely blur caused by diffraction. It will vary by lens, but you probably want f/8 or f/11 for maximum sharpness.

For long exposures, obviously use a sturdy tripod, and you may want to use a remote shutter release and mirror up.

I've been using these sorts of ND filters a lot over the past year. I started out using normal AF, f/22 and a self-timer, and I'd say I had one good shot in ten. Now I use f/11, live view focusing, mirror up, and take more care to make sure the tripod is stable (weigh down with sandbags when it's windy) and my shots are pretty much 100% sharp all the time.