Yes, you can do light and limited milling with a lathe, using an attachment like the one shown on
this page. For newer "non-collectable" lathes you can get one for under $150, but for old Atlas lathes I've seen these for $400+. Of course, you're not making sideplates with this, but most milling tasks are possible, albeit a little more time-consuming (you have to go slow).
An alternative is an
X-Y milling vise for your drill press. You can do light milling with somewhat more flexibility than the lathe setup. Avoid the very cheap ones, they are terribly inaccurate. These are great for drilling accurate hole patterns as well (and often that's the only use they see).
Fair warning: Even if your drill press is a huge industrial beefy monster, this WILL hurt the spindle bearings a little each time you use it, but perhaps this trade-off is acceptable. New bearings are not costly, and the repair is good for the kids to learn. But a drill press is not designed for side loading on the chuck, just know that.
Give yourself some time to find a good machine, maybe a whole year. Find a parent or local business willing to show you the basics (or the trade school option mentioned above). Buy the book "How to run a Lathe" - way old school (100 years ago!) but a treasure trove of excellent data and instruction. Ask here, there are many who would be tickled pink to help.