Our bathroom tile, around the shower/tub, had previously been painted.
We didn't even realize it, as it looked very good. But started peeling
recently, so we decided to try to re-paint it. We sanded the peeling
parts off, which was mainly off the edge of some of the tiles. I
tested one of the tiles with primer and paint, one coat each. It
covers fine in terms of the color, but you can tell where the ridge is
between where the old paint was peeled/sanded off, and where it
remained. I asked at HD, and the guy suggested using lightweight
spackle to raise the lower part and then sand it. I tried that, but
the spackle doesn't stick to the tile very well (if at all; it's
drying now), and it mainly crumbled away. I've always used regular
joint compound for drywall stuff, so this is probably the nature of
lightweight spackle.

Anyway, any suggestions on my situation? I'll try a second coat of
primer and paint and see if that helps, but not optimistic about that.
Should I try getting ALL the old paint off? If so, should I use some
solvent as opposed to sanding, as the sanding of the peeling part
didn't seem to touch the stuff still adhered. Thanks.