However, I have only managed to make this work by keeping the TC in "wired mode" meaning I can't reach the data on the TC wirelessly (e.g. from my MacBook) which has basically downgraded the TC to an overpriced LAN switch.
This tells me that the TC is not configured correctly on the network. Since you probably know the name and password of the "main" wireless network, the problem is almost always found in a non-matching wireless security setting.
In other words, the wireless security settings on your "main" router and the TC must match up exactly. Otherwise, the TC will not behave as if it is part of the same network.....because it is not.
What setting is the Sitecom router using for wireless security?
You mentioned you can have the TC "join" (not "extend") the Wi-Fi network by replicating the same network,
This is one of those situations where the fact that you might be able to do something does not mean that you should do it. I do not recommend this setting. The setting is usually hidden in AirPort Utility. Apple hides it for good reason.
I also notice that Apple has eliminated this option in their Setup Guide for the TC....probably implying that they no longer support this type of setup.
The Ethernet ports on the TC are not enabled at all in this setting, so it is not possible to use them to backup using Ethernet for large backups.
The "double hop" wireless means that backups will take twice as long as normal wireless. This will bring new meaning to the word SLOW, not to mention doubling the chances of an error occuring during the very slow backups.