First, are you sure that Path 1 really includes the inner circle, too?
In the clipping path options, don't forget to check Include Inside Edges...
Can you show us path 1 in Photoshop?
Just found the answer.....
I never knew you could display a path as 'subtracted' in Photoshop If the link above is broken, click on the pen tool in Photoshop and look for the Pathfinder tools in the top toolbar i.e. icons that look like overlapping squares). I guess in previous versions clipping paths were automatically set to cut out the insides so I never needed to know this.
I've been using Pathfinder for years in Illustrator so I feel like a bit of a dunce for not seeing this!
For anyone else reading, I hope this helps!