And some of the tile adhesive is still stuck to the concrete and will not scrape off. Is there anything that will dissolve it? Without burning down the house or making us all pass out?

What are you trying to do once you remove this?

Also, what kind of tile and are you talking about? Cut back adhesive that's black?

The adhesive is white. We are debating leaving it concrete vs new tile.

Rent a concrete disc grinder and make sure the pad has a bunch of grit left on it. This will create a lot of dust so sealing off the hvac vents would be required. After this you can stain. Also look into epoxy as the above may not be required for prep.

I had good luck with a rotary hammer drill and a scraper attachment. Give me a good excuse to buy a tool. I bought a Dewalt cordless and it worked great!

I used a rotary hammer and scraper but we knew we were going back with an underlayment and engineered wood. I ended up with small gauges in the concrete here and there I had to level. Not sure if the concrete staining people can hide those or not but that migh impact a stained concrete floor if you were thinking about that that.