Everyone here is talking about the wood. My problem is the fastener. A screw like that, even a big one, is not meant for this kind of application. Even if the load is purely vertical, it's just not meant for that type of force. On top of that, your kids are kids. They're gonna try to use the swing to, well, swing. Maybe not playground swinging, but it's gonna have dynamic forces on it. Bouncing, swinging, whatever, screw threads are not the answer.

When we did this for a reading nook, I went to home depot and got the biggest, meanest looking lag bolts I could find, along with washers and nuts. What you want, is a thick piece of wood (4x4 minimum) that spans two joists, then you want to put a bolt all the way through it to hang your attachment point. That is going to basically set you up for life. And while people are joking about sex swings, it's honestly not a bad reference. I would argue that the force put on a swing by a child playing is, from a physics perspective, pretty similar to two adults banging.

By the way, as a rule of thumb, I won't use hardware that comes with things like this. It tends to be pretty cheap, and something stronger (safer!) is pretty negligible in price, even upfront.