Replacing VCT tile over concrete and wood subfloor

Have 400 sq ft room above grade; half has concrete floor, half has 3/4" plywood. Previous vct installation failed after 8 years - installer did not prep the plywood portion of the floor, and the tiles have all come loose, even those over the concrete portion of the floor. Pets stay in this room, so puddles sometime occur.
Concrete is smooth and in good shape. Plywood portion is also generally in good shape. However, the concrete portion of the floor is a little higher than the plywood portion - about 3/16". Previous installer tried to ease the transition with some blue felt type material glued down.
I have removed all old VCT tile. I either have to have some way to better deal with the "hump" at the transition, or install under-lament to smooth out the transition.
Questions if I use under-layment:
1. I can staple the underlayment to the plywood subfloor. Do I glue the underlayment to the concrete? If so, what adhesive to use? Or, do I just let it float? If I float it over the concrete, do I float the underlayment over the plywood as well?
2. What to use for underlayment - 1/4 plywood?
3. Do I leave gaps between sheets of underlayment? How big? If the underlayment floats, how do I maintain the gaps? Use spacers between underlayment sheets?

My inclination is to use 1/4 " plywood as underlayment, staple it to the plywood subfloor, and glue it to the concrete subfloor, but this may not be the best thing to do.

All advice appreciated.

 

Welcome to the forums! If you are using VCT as a replacement, you will probably want to use a 1/4" underlayment plywood, stapled to the subflooring. This should get you within 1/16" of your concrete. I would not cover the concrete with any underlayment.
Now, if it were mine, I would consider installing 1/4" concrete backer underlayment over the plywood and laying a not too expensive 12 x 12 ceramic or porcelain tile over the entire area. Much more solid than vct and it won't peel up.