You have a lot to learn about women my friend.
Lets say you get the evidence you need and present her with it. Now she will either feel bad because she's wasted money, or she she will feel humiliated because you've proved her wrong and either way, you're going to get it in the neck.
There's a third option (which is the most likely) in which she doesn't believe the evidence, is convinced it's all wrong and by association it'll be your fault. Get ready for the fireworks.
If you're going to have a long term relationship with this lady then you're going to have to accept you'll be wrong a lot of the time, even when you're right. Plant seeds and let them grow, that way she'll be able to jump to her own conclusions and think that they're hers. This works well with bosses too.