Is there a smartphone, tablet, or some other device that travels with the kids? That would be the easiest solution since MC can sync the video files in the appropriate format to the device. Another option is if there is a computer available at the destination, in which case you could stream to the device via Library Server.
If those options aren't available, you'll first need to make sure you are recording to .ts format in MC since I don't know of any DVD burning programs that can read .jtv files using the DS filter (there's been some work done at VideoRedo, but I don't think it's fully come to fruition). This is a huge drawback since you'll lose time-shifting ability and the ability to start recording while a show is in progress.
The .ts format is tricky in and of itself because it is simply a transport stream for the underlying video broadcast so it doesn't know whether it's encoding a DVD-compatible format (MPEG-2) or something else altogether. Unless you know what you're recording, it's probably easiest to just demux and remux everything to MPEG-2-PS (file with .mpeg extension that can be burned to DVD using practically any DVD burning software). You may run into issues with audio/video syncing.
There are a few ways to do this, some more complicated than others. Here is a tutorial on how to get burnable MPEG-2 files from .ts files for free:
http://arzur.net/2010/05/07/burning-mpeg2-ts-to-a-dvd/Here is software that I can't vouch for that appears to do everything for you:
http://www.mp4-dvd-converter.com/burn-dvd/convert-ts-to-dvd.htmlAnother option is to record shows in WMC and burn the resulting WTV files to DVD in WMC.
I'm sure there are other people here that are more up-to-date on this stuff than me, hopefully they will chime in. I remember some talk about being able to remux M2TS in ffdshow and avisynth--which could lead to an automated command-line solution for you, but I can't seem to find any info on that.
As you can tell, this is an outdated, convoluted process that we are all glad to put behind us out of sight, out of mind. It's far easier to avoid optical media altogether.
If I were in your shoes I would look into investing into something like an Android stick for ~$30 that you could load up with video files and play via HDMI to TVs during traveling without an internet connection.
Edit: Looks like
http://mctvconverter.vivolum.net/ might be a good option to autoremux.