Removal of the vinyl and installation of an approved flooring underlayment panel is not an option? I had similar problems with calcium carbonate (gypsum) based floor patches and skimcoats. We used to add a latex admixture to the product to improve the adhesive properties and help it to bond to problem substrates. I have no idea what the Skim Coat product is made from. Is it white or gray? Sounds to me that you have a poor bond between the Skim Coat product and the vinyl. Perhaps the vinyl in that area is contaminated with something that won't allow the Skim Coat to bond well. That's about all I can comment on here. Perhaps another person will come in with some advice for you. What does Armstrong say?

Sooz, click flooring is not "waterproof". The surface of each plank, and the substrate in the body of the plank and click mechanism are waterproof. But you are correct, some moisture can leak down through the click mechanism especially if you flood the floor (wet mopping etc). But it's a very small amount and I wouldn't think it would damage the underlying subfloor. My concern would be the development of mold, or smell if it's pet urine flooding the floor! The benefit to that kind of floor is it's a bit more forgiving of a slightly rough or unlevel subfloor (sheet flooring is thinner and will transmit subfloor flaws) and it's warmer underfoot because it's thicker. It also can be popped up, cleaned and dried, and reinstalled if you have a major flood problem (sewage backup for example). If you don't anticipate numerous pet accidents or flooding consider a good quality click vinyl such as Coretec. There are numerous Coretec threads on houzz. And they do have tile look options.

I agree that there is no need to remove the old sheet vinyl. You don't need to be concerned with any difference in height (that someone mentioned above) as one layer of sheet vinyl next to carpet won't amount to much at all. Certainly no difference worth noting. If your current floor does not appear to have any bumps or places that stand out as being uneven, and is a "flat" vinyl, then you should be good. The installer should know to check this out thoroughly - if they are any good. Also, if there is existing moisture damage that you know of, then that part you should take a look at. I had sheet vinyl in my kitchen, and was looking at replacing it with ether new SV, or LVT. I chose LVT, Since I had a nice flat floor, the LVT was to go right over the SV, with embossing leveler applied first. Unfortunately, because of the complete idiot that they sent to do my install, the company had to redo the job. (Yes, they lost money on this job.) They had to pull all the LVT up, and some of the old SV as well. (Which I wound up thinking was somewhat of a good thing, in my own mind, because I was able to see what good shape the sub floor was in.) The embossing leveler is even more important, I think, if you are getting a "smoother" type of sheet vinyl than what you had previously - most of the new stuff does not have the shine of the old, and the newer finishes will more easily show any uneven spots that the old SV. (SV really is a very forgiving floor covering - it's why it has been so popular for so many years, and also why so many people wind up disappointed in their "new" floor coverings that they replace it with.) There should be none of the old SV visible through the compound - make sure you ask them about their experience with this. It really is a skill to smooth out and level this stuff. The first guy that did mine did a piss-poor job on that as well, and at the time, I did not know any better. If for whatever reason, your SV is removed, then lay down a good underlayment like these... https://www.lowes.com/pd/SurePly-1-4-in-Whitewood-Plywood-Application-as-4-X-8/50124674 http://www.robertsconsolidated.com/products/accuply-premium-underlayment/ https://www.traxxcorp.com/products/matrixx-underlayment/ Read through this article for more info on underlayments for vinyl flooring. https://bct.eco.umass.edu/publications/articles/wood-underlayments-for-resilient-flooring/ Best of luck. I completely understand your choice of SV - it is hard to beat for wear value and "waterproofness".

Of course its an option to remove the vinyl and remediate the asbestos. It isn’t even a big deal. Sheet vinyl is much less likely to test positive for asbesos compared to the solid vinyl asbestos tiles, so first physically test to be sure that you actually have vinyl asbesos sheet goods.