Were you really counting on a different result because some random person came up to you in Walmart and told you that she wasn't his?

If you truly cannot deal with his daughter and don't want to, leave.

Quit beating around the issues. Go directly to the source and ask the questions directly.  See what your DH has to say when you ask him.

I think as hereiam said - you have to accept that his older child will continue to be part of his life, and if you can't - might be best to leave.

Is your DH upset now that it was questioned? I feel like that would be a normal response. I could also see him having resentment for this being brought up to begin with.

I would suggest counseling. I think that you guys really need to get on the same page as parents and how you want to move forward. I think you should also get individual counseling for yourself to come to terms with being a SM. 

This isn't a life for all women. There is no shame in saying that it is more than you can handle.