I can see my teeth when I smile, but can't seem to see them when I open mouth. Is that normal?

Your upper lip can be internally raised by a periodontist.  An incision is made in the vestibule and some gum tissue removed, which raises the lip.

There are many ways of performing a smile design ,and its not only teeth, also muscles, gums, face design, and smile design can achieve those goals you are asking ,shape, size and color can be change.

Smiles come in many forms and they change as we age. The teeth, lips, gums all play a role. Smile design addresses many of the issues that arise when someones smile is not exactly what they want. There are many factors that go into smile design and creating an aesthetically pleasing smile, both at rest (mouth slightly open) and when fully smiling. Basically you have to create a smile design that works with the dynamics of your mouth movements. Without pictures its impossible to say what is going on with your smile but if you supply some photos we might be able to better answer your question. As far as your question as to it being normal to not see your teeth when you smile, it may be normal for your existing dental anatomy. That doesn't mean you can't change it if you are not satisfied with your current smile. Talk to a dentist experienced in smile design or upload some pictures on this site to get a better analysis of whats going on with your smile.