Hi Kathleen,
If you are struggling to find a dining reservation at the
Crystal Palace now, it will be even harder once you arrive at Walt Disney World.
If you really want to eat at this particular restaurant, I would highly recommend that you make an advanced dining reservation for an available time straight away, even if this is at a time which is earlier or later than you would normally eat.
I would then continue to check for availability each day for a more suitable time as cancellations do occur and you never know your luck.
There is also nothing stopping you from walking up to the restaurant once you arrive at the Magic Kingdom theme park to enquire if there is any availability on that day. (Do remember however that a one-day cancellation policy applies to reservations at this dining venue and so if you cancel within one day of the reservation or if the dining party is a "no show" for the meal, a cancellation fee of $10 per person will be charged to the credit card used at the time of booking.
I really hope that you manage to get a dining reservation at a time which will suit your family.
Wishing you a magical trip filled with memories which will last a lifetime!