""You just remove the loose vinyl portion, or if it all lifts off at once you pull it all. It'll be no extra charge. You just leave whatever is left for a membrane between the subfloor and the tile. We do it all the time.""

If he will not do the job the way you want it done hire someone else to installthe tile. I would not install tile over vinyl, I would think you're asking for trouble.

You are dealing with a cheap unqualified hack. Move On. https://www.ceramictilefoundation.org/homeowners-guide-to-hiring-qualified-tile-installer

No. Tile needs a firm and solid base.

There are plenty who will do the job right

Thanks for your comment. I believe the vinyl is around 15-20 years old, and I have no idea on whether or not we'll have an asbestos issue. We're trying to redo the kitchen and are having a heck of a time getting anyone who'll come out and give us any kind of firm estimate (most of the guys have come in, looked at the floor, and given us a rough estimate). We haven't had anyone look under the house to even see how much weight the floor can hold. It's so frustrating! Our kitchen runs against our wood floor, and so we KNOW there's going to be a height difference between the kitchen and living room. We're trying to minimize that by using Ditra instead of cement backerboard, if we can do that.

We had one contractor who said we'd get down to the plywood, add extra nails for stability if the floor had any flex, put down the Ditra, and then tile. Does that sound right?

THANK YOU so much for your input. I teach kindergarten--this entire process is 100% out of my wheelhouse and has been so frustrating. :-(

15-20 is fine. no asbestos.

as to the plywood (and they should be screws, never nails!)

How are the floor joists? how wide is the spacing? Hows the subfloor over the joists? good condition? all of this will need to be known prior to install of Ditra

Of course you'll have to make sure your floor is level and flat at this point.

In this example they staggered 1/2" ply without screwing it to the joists.

(The joists are rough cut 2 ½ x 8's)

Versabond mortar to adhere the Ditra

Head over to the JohnBridge tile forum and search Ditra flooring questions.

Here's one that compares it to CBU

https://www.johnbridge.com/vbulletin/showthread.php?t=121941&highlight=Ditra+floors

Trades are very very busy right now, and it’s possible that you don’t know how to approach them for work, and they view your project with suspicion because of red flags. You need to figure out if it’s you first, before you move forward. You could be scraping the bottom of the barrel due to wanting to keep this low priced. (It’s not going to be low priced.) You could have a vague scope of work written up. If you don’t have this well specified, you’re not going to get a lot of takers. You also could need a General Contractor. It sounds like the scope of work is outside that of a specialist and includes more trades, and may require structural reinforcement. Here’s a link that will be useful.

https://www.houzz.com/discussions/5332686/10-tests-for-you-and-your-contractor-s-first-meeting 

I don't need it low priced, I need it done RIGHT. We took out a loan to do a kitchen remodel, so we want a quality end result. We haven't necessarily written anything down, but I suppose maybe we need to. I'll check out the link--thanks.