My head canon is this:
Lin isn’t actually Toph’s biological daughter, but is adopted. Lin’s family got killed when she was a baby, and Toph,as the Chief, decided to take her in. That didn’t make their relationship any less beautiful though; Toph treated Lin as her own and trained her to be a topclass earth and metal bender. But, when times got hard or when Toph couldn’t handle things on her own, Sokka would take up the father role.
and then all 3 of them happily skipped towards the sunset lalalla