Let’s say this takes place in season six, twilight sparkle has been having nightmares about that incident at the wedding rehearsal and wished it would never happen. So she comes up with a plan to travel back in time and tells her past self (While hiding her Alicorn wings from her) about The wedding rehearsal and the truth about the fake Cadance. Though she succeeded and the wedding rehearsal incident never happened, consequences followed soon after. So my question is what kind of consequences would there be?

Two options, not necessarily mutually exclusive, immediately spring to mind. The first is that, by confronting Chrysalis at the wedding rehearsal, she actually forced Chrysalis's hand; Chrysalis was going to take more thorough steps to get rid of her, later. Chrysalis is then able to carry out that plan in the altered timeline. The second possibility is that, since Twilight never gets stuck in the mines under Canterlot, she never encounters the real Princess Cadance, leaving her without an important ally/asset when the invasion begins.