Well, you are SOL without buying some stuff. The past few years they have stopped putting tuners into DVD/VCR combos - stupid, but cheaper I suppose.
Your solution to piss her off the least:
2-way splitter, feed one directly to the TV
Some kind of cable tuner box on the other side of the 2-way splitter, then feed that to the VCR input. Feed the output of the VCR to the TV
That said, she won't likely be happy with that either, as she will have to manually set the channel on the tuner box for whatever she wants to record, as the VCR won't be able to setup to change the channel on a timer to do that.
Better options:
- Get a DVR
- Search for an older VCR that has coax in/out
- DVD Recorder with coax in/out. She will probably be super happy with that, and they work very similar to a VCR
The better options will let her do what she likely wants to do - setup recordings for when she is away. What she has now isn't going to pull that off.