Learn Italian: Stavo confondendo tutti e due i gemelli alla festa.

When you use tutti e due (meaning "both") directly before a noun, Italian requires you to include the definite article. Since gemelli is a masculine plural noun, the phrase has to be tutti e due i gemelli.

Could I use entrambi in this sentence instead?

Yes! You could say entrambi i gemelli. Just like with tutti e due, you still need the definite article i before the noun. Both phrases are extremely common and mean exactly the same thing.

Why use stavo confondendo instead of the regular imperfect tense confondevo?

Stavo confondendo uses the past continuous tense (the imperfect of stare plus the gerund) to emphasize that the action was actively ongoing right at that moment. Confondevo would also be grammatically correct, but the continuous form paints a clearer picture of you standing there continuously mixing them up.

Does confondere mean "to confuse" someone else, or "to mix up" things in your own head?

It can mean both! In this sentence, it means "to mix up" because the speaker couldn't tell the twins apart. It can also mean "to confuse" in the sense of making things unclear for someone else, such as saying mi stai confondendo (you are confusing me).