Hate to say it.....but you get what you pay for. Hate to see guys put in all the hours in prep and then buy these Big Box store "Box-o-****" garage flooring kits only to see them fail and peel up soon after install. I'm sure you guys follwed the instructions to a tee...its not your fault entirely...their products just plain **** when it comes to garage floor coatings.
You'll need to grind all that **** off and start over with a quality coating system.
IMHO, take off what you can and go with Racedeck or Porcelain. My preference is porcelain. It is inexpensive if you can do it yourself, and nearly indestructable.
tire pick up has to do with the surface of the concrete and not the epoxy. Either not good enough prep, contamination at those sites, something in or on the concrete
with the proper substrate even the first gen water based floor epoxy (which was used here) would bond fine.
I applied Rustoleum on my garage floor almost 4 years ago. It isn't peeling, lifting, marking, or any other "ing". I'm more than happy with it and plan on using it again when I build a shop next spring.
No matter what coating you're putting down big-box or industrial quality will fail if concrete is not prepped correctly. Correctly, meaning shot-blasted or machine-ground. Also helps to have a top-coat even with the cheap stuff.
I thought about epoxy, but I'm leaning towards racedeck flooring now. It's faster and I have limited parking so I could park in my garage the same day that I install the flooring.