That's called "rivalry" and its like two people talking to you at the same time you can't hear either or only one. It often gets better with time but some are unable to adjust. You may need to consider glasses, contacts or if possible add'n PRK on the near eye but they you would need reading glasses if over 40.
JCH IIMD
If you find that you just can't adjust to full monovision, I have a suggestion that helped me. Try wearing a contact lens in your right eye that will change the focus from near vision to intermediate vision (modified monovision). If this is comfortable for you (and it probably will be), then wear the contact in your right eye for a few weeks (or longer, if you want). When you're ready, try decreasing the power of the contact lens by just a little, and then wear the new power for awhile. The goal of this strategy of gradual change would be to eliminate the contact altogether (and still have comfortable vision). I don't know if this will help you, but I eventually loved full monovision.