This is my big miss as well. I hate the push fade with such a passion that I would rather duck hook one out of bounds than hit a weak push fade. I hate playing from the right trees, also I find the push fade doesn't go as far either, so now I am in the right trees with a long way to go to the hole. I understand your frustration.
For me, it is has all to do with getting my hips forward enough. If I don't get the hips forward then I start to spin them out and either wipe the clubface across the ball with a very weak push fade, or if I throw the club out too far the dreaded shank. If I get the hips forward enough the push fade goes away.
Without seeing a video of your swing I cannot know if this will help you, but it helped me.