I've been using them for years and would recommend the ones specifically made for litter boxes. It makes changing the litter quicker and simpler than using a trash bag, but they are going to be more expensive overall. Litter box liners are a bit thicker than trash bags so ripping isn't going to be as much of an issue, but if it is just double bag it to avoid that problem. Just make sure you have some kind of liner in there and aren't pouring the litter directly into the box.
I see you're using a non clumping litter, but you said you're scooping it still? That could be a problem since scooping out non clumping litter is going to break up their waste into little bits that are going to fall back into the box and mix with the clean litter making the whole box dirty and smelly, which might be off putting to your cats. They won't want to touch old waste, and might be what's causing them to go in the corner.
Your kittens are about old enough now for clumping litter. It's not suggested for kittens 0-3 months old or so since they may attempt to eat it if it gets stuck on their fur. You can wait another month to make the switch to clumping litter for an easier time with litter box maintenance. Until then, I would suggest changing out the non clumping litter pretty frequently. Put in enough so they can dig and bury, but plan on changing that kind of litter much more frequently, like once a week at least but depends on how much they're going. A second box will help a lot with this and I think that plus keeping things clean and tidy for them will solve your litter troubles.
That's a really good point about non clumping litter... I can see that some of the litter falls back into box. If I'm changing litter once a week, do I just dump the litter in a trash bag (don't have liners yet)? That isn't too bad, especially if I don't have to scrub the litter box too much.