1a. These are the wrong kind of TV Splitters. They do not have F Connectors
1b. These are the right kind of Cable TV Splitters. They have F Connectors.
2. Open them by prising off the back. You may need to chip off epoxy glue or solder with a craft blade or sharp screwdriver.
3. The insides exposed. You should unsolder the connections to the case and the F connectors. Don't worry about damage to the back!
4. The insides stripped and ready for the relay.
5. Position the relay so that the "common" contact is nearest to the single connector and the "NC" and "NO" contacts as close as possible to the two connectors.
The two relay pins on the extreme right are the power or coil.
Next we solder on a protection diode (because the relay coil would otherwise generate a high voltage when switched off) and the connections to the pins of the F connectors to the "COM", "NO" and "NC" pins of the relay. You can use some UHU glue or a sticky pad to hold the relay in place.