Time Capsule connected directly to my MacBook Pro
Ok ... does that mean you have thunderbolt to ethernet adapter or just using the TC wifi in standalone mode??
How do you connect to the internet at home when you need it? Clearly you cannot be connected to both the Internet and the TC at the same time!!
Would I be better off to connect it to our home Network?
Very likely yes.. but does the TC actually come up in airport utility in your Mac?
If so then backup should still work.
Did this previously work ok? has something changed?
Mojave should be ok in terms of behaviour. Were your previous backups done with Mojave?