Homemade ice cream texture gritty, sandy?
It sounds very much like you didn't manage to completely dissolve the sugar. It's also possible to get a bad texture from ice crystals in your ice cream, but I don't think you'd describe it as gritty or sandy, just icy.

It can be rather difficult to dissolve that much sugar in liquid, especially if it's cold straight from the fridge. You might want to try heating it gently and stirring, and being careful to go until there's no undissolved sugar hiding at the bottom. That does make the chilling take a bit longer, probably more like 4-8 hours or overnight, not just 1-2 hours. But in my experience heating to dissolve is pretty much standard in ice cream recipes, presumably because it's about the only way to do it easily.

Note that if you do heat it, using only part of the liquid (say one cup out of a total of three cups) is probably best. That way there's still plenty of liquid for it to dissolve quickly, but you aren't heating it all, so you can add in two more cups of cold liquid and cool it back off so it'll be chilled enough to freeze sooner.