It is very occasionally appropriate for priests to remarry a couple in church when both partners are divorced. Priests are legally able to exercise this discretion after suitable investigation, but generally refuse to do so if either of the parties has been a direct cause of the breakdown of the previous marriage(s).
In most cases, priests offer a service of blessing, which usually includes prayers of penitence (with or without a Eucharist) which takes place soon after the couple has been married civilly. Thus the church tries to witness both to marriage as a life-long commitment and to God's compassion for those who for various reasons have been unable to carry it out.
From the information available to the general public, it would seem that if the Prince of Wales is to marry again he should do so in a civil ceremony (changing the law if necessary to make this possible) and then like other Anglicans ask for a private service of blessing with a small group of friends and relations.
Canon ALAN WILKINSON