First, see if you can find new trim and replacement stems for your valve. If you can't, you might as well just bite the bullet and change the entire thing out. Then, depending on what valve you have, you could probably just cut it off. A remodel or renovation plate is likely your friend there, as it can cover the bigger hole you may need to gain access, and cover the old wider spread of the handles.
To drill out the screws, if you're going to throw the valve away, I'd not bother. Only if I was going to try to save things would it be worth the effort. THen, you'd drill through the center of the screw with a drill bit big enough to free up the head once you get through it. You may need a puller to then remove the handle. You typically need the handle off before you can remove the stem.
We still haven't seen a picture of what you have, so some of this is just generic - to get specific, we need to know what you have.