The next time you open a can of paint, or a little before, might be a good time to put on a pair of specs and RTFM.

It may not be the practice where you are, but it's been decades since I've seen a paint can that didn't include specific instructions on drying time and conditions, and fairly specific instructions on what to do if you want another coat.

Oil based paints are subject to quite a bit of variation, and some recommend that the first coat be "fully dry" before applying a second. The majority, however - and most water based paints I've seen recently - suggest that the second (and subsequent coats) should be applied after the prior coat is "tack free and firm" but before the surface is "fully cured."

Some paints, especially those that tout "washable" as a feature, form a surface film that's relatively impervious to vapors and once that film is formed additional drying of paint beneath can be prolonged. Another coat that forms a similar barrier could make curing of the entire (multiple layer) paint thickness take longer than you'd want.

For most paints, the excess of solvents in the new layer will soften the prior surface sufficently that the combined layers will "dry" just like one thick one, with the benefit that the first coat is sufficiently "stiffened" while the "runny part" in the second coat is still fluid enough to "close" the brush strokes and thin enough to "not sag."

If the can didn't include label instructions for second coats, or some sloppy painter who used it before you did allowed the slosh to obliterate them, the paint shop where you got the stuff probably has something similar that is labelled.

If you can't find advice, the most common cause of slow drying (especially with oils) is high humidity. A hair dryer blown directly on the tacky parts might harden them fairly quickly - at least enough that you could feel confident about a second coat. If the sticky spots are mostly where there are "sags" cutting the sags off with a sharp knife is sometimes effective, and the next coat will cover the "correction." Sanding or scraping usually just makes a mess of it all, unless its done after the paint is fully dry; and any use of solvents is likely to make the whole thing "unpaintable."

In the abssence of any corrective action, a "thing for kids" can incorporate "magic spots" that turn the kid a strange color when the kid finds them, and you just tell the kids it's "a prize for outstanding performance." (And then you avoid the mothers until it's forgotten.)

John