Your Piano Expectations Are Too High
If your piano expectations are too high as a parent, your child may not be able to engage enthusiastically with the piano. You have to let the child find it for themselves. Playing the piano requires a very specific set of skills. And that is in addition to talent.
You can play quite well without talent if you take the time to learn the skills. It will be a difficult road, because talent is what will make the journey more enjoyable and a lot quicker. Most kids do not have much talent at the piano. It just does not happen that often.
Some kids will probably always be "fumblers," but most fall into that grey area of medium ability. Let's say 10% are fumblers, 89% are medium ability, and less than 1% have any "knack" for the piano at all. The 1% take care of themselves, given the right teacher. The 10% "fumblers" will keep trying if they have a very patient and sympathetic teacher.
Match Teaching To The Child
But the 89% "medium" talent kids need the most care in order to have a positive experience with the piano. The biggest asset for all these kids is a piano teacher smart enough to match their teaching to the type of child. It takes great wisdom to differentiate between a "fumbler" and a "medium."
Almost all piano teachers treat kids the same way, and use the same curriculum for all. The only difference is the pace at which the information unfolds.
Not One Size Fits All
"One size fits all," is the wrong approach, especially for the slower kids and the "late bloomers," who may take years to develop enough interest to start making progress. For all but the most talented kids, the goal is to keep them at the piano, enthusiastic and interested.
It takes great skill on the part of the teacher to maintain interest at a pace the child can handle, but a faster approach always leads to disaster.
Who cares if a child takes years to learn a few skills and a few pieces they enjoy to play? The goal is to not rob their future attempts at playing the piano by starting too quickly and leaving the child's feelings in the dust.
If you go too quickly your "method" will have succeeded at winnowing out a weak candidate. But the child will have failed to get any reward from the piano.
Sow The Seeds of Further Interest
Think of the child at 15, at 25, at 35, and imagine that you are sowing the seeds for them enjoying the hobby in their future life. Just because a child fails at the piano today does not mean they cannot succeed wildly at some time in the future.
Today's lesson is irrelevant, what matters is the possibility of them playing in the future. Don't rob kids of that possible future by moving faster than they can enjoy.