Adding second battery to setup

Hi all, I currently have one of these and it works well (https://www.sustainable.co.za/omnipower-power-caddy-iii.html):

I'm looking for a way to add another battery though, what I was thinking was to:
- Get another empty box and add another 105AH battery into it
- Have the positive and negative leads coming out on maybe a Brad Harrison type connector
- Then on my original box with the inverter, open the box and connect another set of leads to the +'ve and -'ve terminals, also coming out of the box on a Brad Harrison connector.
- Thus connecting the two batteries in parallel

That way I would be able to disconnect the second battery box should I need to take the smaller setup with me, so I don't lose portability - but still have the benefit of more storage.

I will of course need to consider age of my current battery, and also not running the main battery box on it's own too often.

A few questions for those with some experience:
1. Is this a bad idea?
2. If I take the main box with me somewhere and use it till it's dead, but the second box is fully charged - what happens when I come home and connect it together again?
3. The existing wiring from the battery to the inverter is quite substantial, I don't think the connector into the inverter will allow for a thicker wire. Would this be an issue?
4. What size wire and connector (size or alternative type) would you recommend to go from the main to the secondary box?

Thanks a lot