If you have an Apple Store within easy travel distance, it is well worthwhile taking the phone and SIM card in to them to sort out.
Try a factory reset of the phone with no SIM card inserted and only insert the home SIM card after the phone has been reset.
The SIM card works fine in another phone and previously worked fine in the iPhone, so individually each device is probably working correctly. I would theorise that some data is being retained in the iPhone from the travel SIM which needs a full factory reset to remove. You will lose all the data on your phone with a factory reset, so make sure all data is backed up using iTunes or the cloud, as detailed in Apple's instructions.
Make sure you have the latest version of iOS installed, it should be 10.3.3 or higher. Go to Settings, General, Reset, Erase All Content and Settings.