No, I think not. Was the old floor covering stripped of wax prior to the installation of the new floor? Does the manufacturer recommend (or not) the installation over an existing floor? Is the adhesive warranted for this type application? See how this works: we keep asking questions until there are now more answers to be had. Should the existing floor covering be embossed or skim coated prior to the new floor installation? Does the old floor covering manufacturer even recommend this type of installation? To answer many of these questions, you must know who installed it and what the old floor covering is. If you can glue atop an existing vinyl floor, is the trowel notch the same for all substrate? I would think not. Porosity of your substrate and the floor covering backing must be taken into consideration on all job sites.
Photo 4 shows a 1/16-by-1/16-by-1/16 square notch had been used. The recommended notch would have been 1/32-by-1/16-by-1/32; the difference being almost twice the amount of adhesive was used than should have! This will also affect your open time. If you don't allow the water in the adhesive to flash off or give it an opportunity to let off gas, you will trap it (the gas) between the impervious vinyls. One or two bubbles can be dealt with; seam sealer and a hypodermic syringe works best. But with the amount of trapped air in this installation, it would take more than just a stitch-n-time to relieve it all.
Removing both layers of vinyl at this point is the only option I know that will work for sure. Thanks for reading, and have a great day!