Removal of lime from a garden pool be used?

We have a small pool in our garden not been used since years. We except the old dirty water and gave it a good cleaning but it is a collection of minerals that do not want to come. We have tried lime descaler supermarket does not seem to do the job. I know he more other products on the market, but I am concerned that harsh chemicals can damage the film. All thoughts and suggestions appreciated.

Vinegar so it works on the starting grid of lime will be OK

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