If your husband picked out the e-ring all by himself without any input from you and you didn't like it would you ask to go shopping with him?  
I think the short answer for me would be 'no' I would want the ring he chose for me and proposed with.  But I think if it was something God-Awful like something I could never in a million years see myself wearing, I would have to break it to him gently that we may have to go back to the drawing board.  To be honest the e-ring he picked for me is not exactly what I would have chosen, but it's beautiful and he chose it so I would never want another.
DH told me that he went to a few different stores before returning to the original one to buy my e-ring.  When he walked in the woman who had been helping him previously said the diamond he had his eye on had been sold.  The lady said the guy buying it had returned the original e-ring because his FI told him she wanted a bigger diamond.  
                 
                
Re: Another Ring Question...
However, we both are really picky about how things fit and feel. I think style-wise he could have done a good job, but I wanted a ring that had a low enough profile so I could still get my hand in my pocket while wearing tight jeans. Also, I have long hair and some settings can catch your hair a lot.
Likewise, my H is a construction worker and he needed a ring that would feel right on his hand while he's working with tools. And something that can be cut off in an emergency.
DH picked out my ring alone, but he used to work in a jewelry store. He had a good idea of quality diamonds, which were his first priority. Style was secondary. If I hadn't liked it, I think I would have found another setting with him. After 7 years though, he knew my style pretty well.
I don't think I could wear a ring possibly for the rest of my life if I didn't care for it. I know someone in this situation, but she's not sure how to approach changing it now. It' been over a decade.
C 7.16.2008 | L 11.12.2010 | A 3.18.2013