imho, the act of the father giving away the bride is symbolic as it means a woman leaving her family and forsaking all others to become one with her husband.
i feel that if you have actually went through some marriage procedure e.g. rom already, it may not be appropriate. but it's perfectly fine if say you're having solemnisation at the dinner itself, and the father is showing to the world that he's entrusting his precious to another man.
another way to involve the parents could be to get both sets of parents to march in before the bride and groom. i like it cos guests will be introduced to the VIPs, the hosts for the dinner at the very beginning. It also gives our parents some sort of recognition for without them, the wedding would never have been possible.
but, it really is your wedding and you may wish to have it the way you prefer
just my thots