A matter of trust

I have had trust issues since I was a much younger man. I can't really say what caused them. Maybe a single incident--maybe more. Be that as it may, my life since then has been one in which I have been skeptical of many things, including things people say they will do, or have done. Counterpoint to that though is that I have largely been religious my entire adult life, for most of it as a Mormon, and the last several years as a Bible-believing Christian. So, obviously, some manner of faith has been involved in accepting those differing belief systems. And while early on I  found myself doubting some of the tenets of Mormonism and eventually all of it, I have never doubted the existence of God, nor that Jesus Christ was my Savior.
But still, I sometimes fall into a lack of trust in God. I find myself telling God that certain things are too tough for me and that I need him to solve the problem, because I have no answers. And then I forget about what I just asked God to do, and go about trying again to solve things that I have found myself unable to solve in the past. In effect, in those situations, I have given up on God or been too impatient, and I have waded in, both arms swinging, trying to dig out of impossible situations myself.
It's not that I don't think I should keep trying. I do. I have always believed that a man who quits is someone who is not to be respected. I post motivational quotes around the house and try to live up to them.
But how does that involve God? Is my impatience in God's timetable admirable because I want to get things done and I feel the need to keep on fighting? Or is my lack of faith a weakness that stems from my trust issues of the past? Why do I sometimes feel that I can only count on myself?
Deep down, I feel like I need to relax and trust. It's what I want to do. It's who I want to be. I believe strongly that God is there listening, and now I know that I never deserve help, but that God, who sacrificed himself for me on the cross, made me whole and continues to do so. I can trust in that. And I can trust that a God that mighty can do pretty much anything, including healing my distrustful heart. That is what I will ask him for. I don't deserve it, but I know that what he wants for me to. And that is good to know.