A parent's view of Sport is as different from his child's as the view of an eagle is from that of a flying squirrel. A skater approaches her sport as a mix of social challenge and self disciplined excellence. For a parent though arriving at this point in time was an up and down roller coaster through a social circus, a dating jungle, the medicalised and worry-prone years of birth and then raising a toddler. By the time a parent achieves the point of getting a kid into a sport, they have essentially already been an evolutionary success (in the sense of accomplishing the purpose of our specie). So it's not unusual that a parent views sport as a surrogate to introduce their child to simulated challenges that parallel and prepare them for the actual life they must still encounter.
A surprisingly large part of this parenting happens on the road. I already did a couple of other posts (here and here) about the amazing preparatory experience of packing, driving, and arriving at the rink. The trip home after a tough competition however is a whole 'nother animal. More than anywhere this drive home is where most of the "heavy parenting" occurs.
If it's been a tough or frustrating day your role should be to lend gentle support, as well as offer solace for any physical requirements (stopping for food along the way seems to be a common desire).
Even so love typically dictates that you avoid speaking directly to onerous issues: it would be both crude and counterproductive to ask "what seems to be the problem with your camel spin today?" A much more useful conversational opener however might be "How are things going?" If your kid says "I'm having lots of trouble with my camel" then certainly listen, but don't cross over the line to pry with "maybe you should blah blah blah." The point is to help her discover her own path, whatever that might be, not to step into the skates of her coach. "What do you think" or "how could you find out" are great prompts to advance your kid's thinking along.
Parenting after a competition can really be quite a sublime challenge from another dimension. Individual parenting styles may be quite dependent on personality. I'll try to describe my own way of addressing the post-competition drive in some detail, yet I don't claim a "right" way in the matter. Frankly each parent has their own approach grounded in their personality, so this is just mine.
My underlying premise is that a child faces nearly as much danger if you falsely build up her ego as if you recklessly tear it down. You want to buffer your kid to any feelings of frustration, to encourage her to overcome and find the strength to persist and continue to strive forward. Yet you don't want to invent an imaginary environment where you might be deceiving her into thinking she will falsely be able to entertain a range of experiences beyond the actual capabilities within the realm of her physical ability.
In other words, always aim for balance. If your child is feeling overly proud, gently take her down a notch or two. If she seems to have lost hope, encourage her to persist.
If you're in the car with flowers and a first place trophy then gently congratulate, "that was a cool skate," and allow your daughter time to savor the joy for a while. Later in the drive though bring up some of the other nice things you saw at the competition, so your daughter won't feel so smug and self centered. You are gently letting her know that she did well and that you are happy for her, and yet this is just another step on a very long path. There will always be better skaters and more techniques to learn.
If you find yourself in the car with just a skate bag and a sad little girl, then respect her private thoughts, but don't throw in the towel either. You most know yourself in your adversities; the kernel of disappointment teaches her as much as the daily struggles to understand the physics of her body. Make a nice comment or two about the highlights of her program, letting her know that "the blah you did was one of the best I've seen you do," and listen to her concerns. No, really listen. Life is larger than skating, and this is where it all comes out.