Repairing Kohler Purist faucet - help please

[Kitui]

Hello, my husband says that to repair the two handles we need to remove the counter top from the cabinet. It sounds weird to me but I thought it was a good idea to ask here. The sink is over the counter top (drop in). I have added a pic of the problem (water flow from the handles bottom). If we do not have to remove the marble counter top, any suggestions on how to go about it? Thanks for helping

 

[WorthFlorida]

You do not need to remove the countertop for any faucet.

https://support.kohler.com/hc/en-us/articles/360002210494-Remove-the-Handles-for-the-Purist-Faucet
Remove the Handles for the Purist Faucet

1. Hold on to the handle while turning the handle base or skirt counterclockwise by hand or with a strap wrench, taking care to protect the finish.
2. Remove any remaining components to expose the valve. ...
3. The valve can now be replaced or other repairs made.
4. Reassemble handle parts in reverse order.

 

[Sponsor]

 

[Kitui]

We could remove both handles, however the right valve does not want to come out. It is spinning and even though we hold the bottom with a wrench and try to move the top with a deep socket...it is not moving. We are concerned about breaking the copper pipe connection. It is a crazy tight space! what do we do?

 

[Reach4]

what do we do?

WorthFlorida said to leave the handle on, and hold the handle while you turn the base.

 

[Kitui]

WorthFlorida said to leave the handle on, and hold the handle while you turn the base.

The problem is not removing the handle but the valve. Unfortunately is the valve that does not disengage from the rest of the faucet bottom part