Honestly, I'm not being nasty, but I think she's just not very bright and she thought the BBC could stop him sending her son money, because she doesn't know how these things work? We can speculate on her motives in going to the BBC then the press, but I think the most straightforward explanation is just that she's not bright and she thought the BBC could stop HE, so when they didn't, she felt like she'd been wronged.
If this whole story is true, I definitely feel sorry for her. Loving an addict is horrible. I'm just saying that I think her actions seem odd because she misunderstood what her actions would cause to happen.