I thought about that too, and you're right, it may place her in a very difficult position. But if this is his last trip to the UK before he leaves office, then I actually think he will meet her.
And if the purpose of Obama's visit is to support the British Government in its aim to stay in the EU, then I think it will backfire, because he isn't exactly popular in the UK. There are not many Brits who will listen to what he says.
This is not a political forum and I'm not trying to start a discussion about Obama here, but I don't understand what Brits have against him. I actually like him and thinks he's been a fairly good president (especially considering the economic situation when he took office.)