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Peeling thermofoil doors is a verry comon problem. Your shortest way to fix that problem contact a local cabinet maker or kitchen showroom. Select desireble and available new door style and finnish. (I would recomend Shaker style just because of Value of this door). Get estimate for refacing and choose contractor you vant a work with.
Da Vinci Cabinetry
Manny Stiega
This is not exactly an answer, but I just installed thermofoil doors and drawers at a cost of 30K. I hope your doors are old because this question got me worried.