A pelham and a double bridle are very different. Generally with hunters people will try and use a snaffle and if that's not enough bit then they will switch to a pelham for the extra leverage. The reason why some people might think that a pelham will be a tie breaker is that the judge is looking for the horse that looks like the nice easy ride that will float along down the lines with minimal effort and they might get the idea that the horse is hard to ride if it goes in a pelham. But I agree with what KayKat is saying. It's better to have a really nice trip in a pelham then a mediocre trip in a snaffle. If your horse goes better in it, why not? But if your trainer thinks its best to put her in a D ring I would try schooling her in the pelham to get her tuned up and switching right before. Altough watching the video it didn't look like most of those horses were going in a great frame anyways (I see a lot of head tossing, inverted necks, nose poking, etc) so I wouldn't stress about it either way, I think Sandie will be fine. PS, I think I say this every chance I get but she is ADORABLE and I love her. ;)
The point of a pelham is that it's a less sophisticated double bridle - it doesn't have two separate bits, so you don't separate the action as much, but it is supposed to ride like the combination of a snaffle and curb. It also has less disastrous results if used improperly, and is less metal in a horse's mouth - very useful as a halfway stage between a snaffle and double bridle. There are always some horses who work great in a double but need the curb action separated so never pick up the contact properly in a pelham (like my horse), and there are some who find the double simply too much metal in the mouth, but in general the traditional showing progression of bits is from snaffle to pelham to double bridle in terms of training.
When we show hunters here, accepting the pelham or a double bridle (both can be used in the show ring, but you see more pelhams than doubles) is a sign of having a mature mouth. If the horse looks like it's carting round and needs the leverage to stop, then obviously it won't place as well as a good horse in a snaffle, but a horse working well, properly accepting contact and working in an outline in a pelham is going to beat an equally good horse in a snaffle here as it's just a sign of having reached the next level of training. Traditionally, hunters were ridden 'on the curb', and whilst that isn't the case now, a pelham or double is still the correct way to bit hunters here for showing, unless they need a snaffle as they haven't reached the point of accepting a pelham or double.
That's here though, and I know things are pretty different here. I can see why needing a leverage bit to control your horse would be frowned on, but I struggle to understand why you would be marked down if your horse went nicely in a pelham. Crazy old showing, huh?