If my eyeglass prescription is +4.75, is a polycarbonate lens going to be too thick for plastic frames?

Your optician can give you the best answer on that. I do not even know what a polycarbonate lens is. I expect him to know that. I do know, however, that more powerful prescriptions that normally produce thicker lens can be made from materials that will give you a thinner lens. Costs more, so depends on your choices.

I don’t know what type of lens my sons have but their prescriptions are above 5.0. We get the thinest lens we can to avoid the coke bottle glass effect.

Nah. My old roommate is legally blind, but she has adorable, thick plastic frame Prada glasses. Just like these.