Is ablution considered valid if water did not reach a part of the foot in the first wash, and this was completed in the second and third washes with the intention of completing the wash, not repeating it as a Sunnah, and only interleaving the toes in the first wash?

The part of the foot that was not reached by water in the first wash is sufficient to be washed in the second or third wash with the intention of fulfilling an obligation. Some scholars even permit this with the intention of a supererogatory act. And interlacing the fingers of the hands and feet is a Sunnah according to the majority of scholars, and it is achieved by performing it once.