Time to put on my cold-hearted, mean old umpire hat...
As the umpire, you don't have any choice but to accept the appeal. A rule's a rule and we don't have the luxury of picking and choosing which ones we want to enforce to make players feel good about themselves. Anything less demonstrates a lack of honesty and integrity.
Having said that, I would have a couple of questions about this play.
- Was the umpire 100% sure that the player missed the plate? On a missed base appeal, the umpire should NEVER "guess" at an out. This is a call you don't make unless you are CERTAIN you saw the miss.
On a home run the plate umpire should always be positioned near home plate as the runner crosses it. At that moment his only priority, duty and responsibility is watching the runner touch home.
- What rules are you playing under? Depending on the sanctioning body, this is NOT something that can be appealed by a coach. The appeal must come from an infielder, either with or without possession of the ball, since it is a dead ball appeal.
While the umpire is obligated to accept the appeal, he is not obligated to accept an improperly executed appeal! If the appeal is not properly made, it should be ignored.
Beyond that, from a coaching standpoint you should always tell your players to stay back from the plate as the runner crosses it. If you give her room to touch the plate and let her touch be obvious, it takes away any guesswork or judgment on the part of the umpire as to whether the plate was touched or not.