according to the wisdom of my children) it's a bit of a race to see who can stick it in the other one first, in order to make baby snails. Whoever is the winner (their word) gets to pass on the seed and the other then has to carry and lay the eggs. Disclaimer: I have no idea if they are right.
They are broadly correct. It varies by species. For a start, not all species are hemaphrodites, and some of the ones that are will - under the right conditions - self fertilise rather than mating.
When hemaphrodite snails do mate, they usually both transfer sperm, and then produce eggs for the sperm they receive. However, producing eggs is metabolically costly so they have an immune-type reaction that destroys at least some of the received sperm. The ideal result for an individual snail is that all the sperm passed on meets and egg, and all the received sperm is destroyed - but of course if all snails were equal this would result in nobody producing any eggs and the species going extinct. So it's an arms race of stronger sperm and better immune systems and in any given mating 1 snail will have an advantage but overall it averages out.
But some species have also evolved a small calcium harpoon, which they attempt to fire at each other. Both snails in a mating pair will have this, but whoever is hit first doesn't get to fire in return. And the harpoon injects countermeasures that prevent the sperm destruction - so the successful shooter ensures its target will lay more eggs.
Slugs have slightly different systems. They engage in penis jousting and the winner gets to be the penetrator.