So, how do you relax the string hand and forearm? First of all, to do that and many other things in archery, like use back tension, keep your head still, know if you're creeping, etc., you have to be physically aware of what your body is doing. If you want to do something, like relax your forearm or keep your head still, your body will do it for you when it figures out how to do it, just like a good dog would, without having to force it. What you have to do is to learn to notice (be aware of) the movement your body is making. That's all. If you're aware of whether your forearm is tense or not, and want it relaxed, your body will learn to relax it.
So how do you learn to be aware of these things? This goes way beyond archery. In fact, more people use archery as a means of becoming aware than use awareness as an means of learning archery. The first rule of awareness is that you can't be aware of what your body is doing if you're thinking about something. It's impossible. So open yourself up to awareness by ceasing cognitive thoughts while you are shooting. Focus your attention on the body part you are concerned with while you are shooting the bow. Eventually, you will begin to feel whether a muscle is tensed or relaxed, your head is moving, etc.
A coach could stand there and tell you, but you're not always going to have a coach next to you, so you're going to have to learn to do this for yourself. What a coach is good for is pointing out things that you don't even know you should be aware of. He can't fix them for you.
So for your purpose here, know that your string forearm and hand have to be as relaxed as possible while you are holding the bow at full draw, and you have to relax your string fingers to release the string. You have to figure out the difference between relaxing your string fingers and opening them. Hint: just because your release is a surprise doesn't necessarily mean you are relaxing your fingers, although it's a good sign.