Yeah, cheap headsets FTW (but maybe not TOO cheap?).
The other, more trouble-free option, would be to outfit each of their PCs with a webcam with decent audio, such as one of Logitech's with "RightSound (tm)" audio, like the C525 or C615 models (auto-focus too), and then get each one of them to get a Skype account, and put each other on their friends list. Then all they have to do, when they start their gaming sessions, is launch Skype and log in, and they'll be connected, no need to set up your own TeamSpeak server, etc., and no PTT.
You would also of course, need speakers or monitors with speakers built-in (HDMI is good for that).
Downside, is that chatting may not be so clear, with the game noise in the background, and you'll be able to hear their game noises in the house. Upside, is that the webcams take basically NO maintenance, and should last a good long time. (No wear-and-tear from putting on and ripping off headsets, yanking cords, etc.)
Edit: I don't know how old they are, but the other downside is, you might find out that they suddenly acquire "online girlfriends" several states away...
2x of these, $30 ea, REFURB, would do it.
Edit: Disclaimer, I don't have kids, but I've gone through a few headsets, and honestly, for extended gaming or chat sessions, I always find them somewhat uncomfortable. Webcams are pretty non-intrusive, sit on top of the monitor, and just work.
Edit: Another thing that you could do, to make the chat audio clearer, and more separated from the game audio, is if their PCs have both regular analog speakers from the mobo's audio out jack, as well as HDMI audio through a monitor with speakers. You can adjust which device outputs which audio (in most cases), and set your skype audio to the HDMI monitor speakers, for chat, and set the game audio, to the more "booming" external discrete speakers. Recommend a good Logitech Z323 or Z313 2.1 setup. Refurb to save money, of course. Booming sound for $20-30.
Edit: Also to clarify, Skype will work for voice-only (not video) chat as well, with headsets OR webcams with mics.