First off, sorry to hear that you're in this situation. That's an utter joke.
Secondly, there's a child at stake here. No one, regardless of the relationship between the parents, should ever miss out on the right to seeing their son/daughter.
Definitely get some form of written proof from her ex about what he's claiming then lawyer up. Maybe even speak to the likes of citizen's advice, they might have more knowledge of legal stance here. After you've got that proof from the other lad, I'd confront her calmly. She seems pretty volatile (and utterly vile if she did fake the DNA test) so approach with caution. If that doesn't get you anywhere then go through the courts. It'd really be a shame if that's what it came to, but best of luck mate.
Poor kid.