Answer: Digging when the ground is wet is not optimal, but it sounds like your only option. When digging up the shrub, dig up as much of the root ball as you possibly can. Wrap it in burlap or wet newspapers until it gets to its new home. Plant as soon as possible, it would be great if you could work some organic matter such as compost or composted cow manure into the new planting area to help nourish the traumatized plant. Keep in mind, this is an offense to the quince and it may "pout" a bit this season by not flowering as beautifully as it did previously. It should recover the following season though if given a little TLC.
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