I love having children at weddings, but not every wedding loves children! I have been to some where they were woefully unprepared and one where they where so over prepared that the children where whisked away to the creche so quickly they missed all the photos! The only person less pleased about that than me was the bride (as you can expect!).
However if its mummy and daddy getting married all of sudden this normally independent toddler that you cant cuddles for love nor money, suddenly becomes incredibly grumpy and stuck to mummy's inside leg! "Why, why today" I here disappearing brides say...... well I have a theory.......
How do we feel at weddings? We get emotional, we want to cry with happiness, we cant stop it but we can process it and laugh it off. However for the child of the couple, they know that they feel emotional but they don't know why. That child can feel the tension, they can feel the changed in atmosphere but they have don't have any idea why it happening and so they act on those feelings.
So my advice...... don't get cross with them! Give them a cuddle, tell them its an exciting day..... and then get someone (not the grand parents) to be there to take responsibility for the child for the duration of the day. If you have a baby sitter or a nursery worker they may be a good option. You need someone who wont be emotional attached to the proceedings, who can occupy the child just far enough away to keep them involved in the day, but not so involved it get too much for them.
I personally would not suggest they are left at home as the 'earth mother' feels they should be there. However for the sake of a days wages, your mind will be a rest that someone else is responsible for the child. Not only for the emotional care but the practical care too. That responsible adult will be make sure they eat properly, sleep when they need it and nurture them during the day so, the parents can enjoy a wedding day stress free.