whose name was Shua

Shua is a Canaanite woman who married Judah. (See: rc://en/ta/man/jit/translate-names)

he ... went to her

This is a polite way of saying that he had sexual relations with her. See how you translated a similar phrase in Genesis 16:2. (See: rc://en/ta/man/jit/figs-euphemism)