i used to be the same. My left wrist would always give way long before my right when doing heavy dumbell bench or shoulder press.
What worked for me was doing forearm excersises a couple of times per week and use straps on heavy sets only for a few weeks. Now i dont need them at all.
Also try some grip strength excercises. They will help to strengthen joining muscles in your lower arm as well as your forearms.
Another tip is, when doing single handed dumbell work, always lead with your weakest hand, if you fail on say rep 7 on you weakest hand, dont push past that with your stronger hand. That will encourage even size and strength gains.