I can't inspect your jobsite, but from your description I can venture an educated guess: Your house is built on a concrete slab and that concrete is emitting moisture. That moisture is condensing on the vapor barrier and is resulting in the liquid water you see and, consequently, the mold and mildew growth.

Before you install any new flooring product, find a flooring specialist who is knowledgeable about moisture and concrete and who can give you a prescription for correcting the problem. Lots of ways to reduce moisture transmission through concrete...the least costly being to correct any standing water issues outside the house near the foundation by providing roof runoff pathways to lead water away from the foundation and even by removing plantings that may be contributing to the problem.

There are topically applied moisture barriers in both liquid applied and sheet versions that we use to 'seal' concrete slabs and prevent moisture migration.

You might have to install flooring that is not a vapor barrier.

glennsfc, thank you, yes that is what happened. We will be tiling in the kitchen, and afterwards taking up the flooring on the other side to see what's going on inder there. No other option.

Glennsfc, as always, pretty much expertly summed it all up.

I will only add that a penetrating sealer be used in multiple applications if required. Non or less penetrative sealers can be blown off by excessive hydrostatic pressures becasue tehy do not penetrate as deeply.