ok, coming from a girl... dont obsess so much over the ex and just because there are problems or what not in a relationship doesnt mean that it is a "someone else" scenario -she is probably not cheating. her and the ex -they broke up- there is a reason people break up and so trust that that reason is still there and that when she insists there is nothing between her and the ex, she is telling the truth. she is dating *you* not the old guy, that means she picked you, and the fact that he is so keen to get back together and she still picks you should put you on top of the world, not threaten you. if you get possessive and jealous it will do little good, and then she will {as she has} pull the 'space' card and dodge you. let her know you trust her and give her the space she needs and then, do just that, believe in your relationship and more importantly, Her. if you want it to last you need to trust each other and make one another feel secure.
and if she insists on being friends with him, just ask her to be honest with you, because honesty helps to build trust. and then respond in a mature fashion because that will show her that it is ok to trust you too

well, its what i would do
hope it works out for the best...