I can't recall if you mentioned if you are in therapy or not, but by the way that you a speaking I don't think that you are. Coming out to your mom and dad is going to be hard as it's difficult to gauge what is worst for them, having a son who is gay or a son who is TS. The other point is that you can't be telling them that you "want to be a woman", as their answer could simply be "well you can't". Remember that simply wanting to be a woman doesn't make you one. You are either a woman or you are not.
As your dad already suspects that there is something wrong and that you are possibly gay, the best way to approach this is simply tell them that you know there is something different about you and that it feels as though you were born into the wrong body, that the way that you feel is not right, not the way a boy should feel, or words along those lines. You also need to tell them that you need to go into therapy to help sort these issues out. Now you may be gay and that is a different kettle of fish, and has nothing to do with being TS.
Although you said otherwise I'm pretty sure that you did leave out your female cloths, and that subconsciously you probably wanted your dad to find them. I believe that it's something that we have all done in the past as away of giving the world a peak at the real us.
It seems that your mom is sorta OK but she could probably side with you dad if push come to shove. Just be careful and when you come out, come out to them both at the same time. Be prepared for some ridicule, some denial, but be sure that you are prepared with the right answers, don't be wishy washy about yourself. Be positive and upfront as they are probably going to want to know what this all means and where you are going to go with this.
Just some thoughts to wrestle with.
Steph