isindie lovely woman, here are my suggestions - feel free to ignore 
Firstly don't make your not-drinking into the main issue of the day, you're not signing the pledge, it is only ONE day sober - and you and I know that you can manage that. And don't make your parents into the main issue of the day either.
What your day is about, is the public commitment that you and dp are making about your love and your relationship and your intentions for you and your little family. It takes some of your private, unspoken matters of the heart, and dares to say them out loud and celebrate them . And I would dare to suggest that being sober is a pretty damn good way to show your commitment on that day - it is about you and dp making sincere pledges and celebrating your love - everything else that is going on around you is a mere distraction (whether it is good or bad).
So prepare for your non-drinking in the same way as you would prepare for any other important aspect of your wedding - the most risky thing to do is just vaguely 'hope' that things will turn out OK. You won't be vaguely hoping that your vows turn out OK, or that the catering arrangements will be fine on the day, or assume that the weather will be sunny and dry - I imagine you have discussed them, made lists, planned, delegated, agreed, maybe even made some contingency plans. Could you do the same for being sober?
Start the day before - plan some relaxed time with dp (if that's possible), plan to detox, pamper yourself, keep your hands busy, iron your clothes, arrange some flowers, write a last-minute love letter to dp. Actively have a detox plan with fruit juices, camomile tea. Lock all alcohol in the cellar. Enroll a couple of friends / dp into join you and support you - plan a contingency so that you know how you will respond if your dsis turns up with a couple of bottles (you are not refusing to drink with her for ever, you've just decided that you don't want to have a crap night and wake up hungover on your wedding day).
Then on your wedding day, refuse to get into the champagne drinking while getting dressed - however kind other people might think they are in offering it to you, you know that it will make you burp and red-faced and sweaty, and leave that horrid taste in your mouth a couple of hours later - not the look/feel you want on your wedding day. Maybe your dsis will be disappointed that you are saying no, but it is not her day, it is yours and dps, so just this once you get to prioritise what you need.
For the rest of the day, make sure you always have an alternative, better choice whenever anyone offers you a drink. Could you delegate a friend to have the constant responsibility of always making sure you have a supply of iced sparkling water with a twist of lime and fresh ice cubes - that should be his/her sole responsibility, and as important as keeping the rings or making a speech.
Know that you are not missing out by not having a drink - there is every other day of your life for that, if that is what you want. The champagne you don't drink on your wedding day will not magically vanish - you could drink it the next morning if you wanted. Or drink it late that night when you and dp are truly celebrating your glorious day in private intimacy, looking back over the day, reflecting on delightful moments, being clear-headed enough to remember every look of love, and reassuring touch that had passed between you during the day, and knowing that even any stupid or thoughtless comments could not penetrate the circle of love surrounding you. [soppy cow emoticon]
And finally, my recollections of weddings are that they are really crap drinking occasions anyway - you get half-drunk during the preparations (not enough to really let your hair down, but too much really - leaving you sticky and yucky and wanting more / wanting to sleep); then the rest of the day is a frustration of half-drunk glasses before you're called away for the photos; or empty glasses because the wine waiter is at the other end of the table; or feeling that you can't drink too much because all eyes are on you; or irritation at having to dance and circulate with all the guests rather than sitting in a corner with a close friend getting pissed.
Dear isindie there must be something in that epistle that you can use