Whats up holidaygirl, since all the tiles are already lifted and the paint is beginning to peel it shouldn’t be a very difficult job at all. That black tar like adhesive your mother had painted over is black mastic, before anything take caution when dealing with it because in the past they would combine the adhesive with asbestos as well as the tiles they’d lie on top. That being said to best way to remove the old paint and adhesive all in one step would be to get yourself a good thick scraper or floor scraper and some flooring stripper. The flooring adhesive stripper will need to be brushed on with a natural bristle brush and left for ~15-30min as it dissolves/breaksdown the paint and adhesive. Once the time is up scrape up all that old stuff and get the floor as clean as possible, you will then brush or roll out a concrete etcher again this can be some nasty stuff so take caution when using it. Once the floor is stripped, etched, and almost ready for paint you will want to apply a concrete primer, these are usually clear in color and thinner than most paints but they will ensure a long lasting perfectly bonded top coat for your next step. Lastly you need to pick out you color choice and sheen and its time to paint. Apply it like you would any other paint be sure to follow instructions as some require two light coats others may just want one coat, and there you go you will not have to worry about that paint chipping or peeling for a long long time. If you have any questions post em up and well do our best to assist you.
Jeff With [URL="http://community.homedepot.com/"]The Home Depot[/URL] Chicago.