If you want to switch the 12V feed to a 1kW inverter with a relay, it will need to have contacts rated for about 1000 X 1.2 / 12 = 100A continuously. This is a larger relay than normally found in automotive applications. Don't use a plug-in cube style relay no matter what current rating it claims. You want something with big bolted terminals. Also, inverters usually have large capacitors across their inputs which cause inrush when the circuit is closed. This tends to weld relay contacts in the closed position, unless they are amply rated for the purpose.
However, the relay might not be needed. Many inverters have a remote-enable / control switch function, that allows control via a small switch carrying a fraction of an amp. The battery charger can remain connected permanently to the battery, although if it includes a voltage indicator that remains on all the time, it might create a small drain on the battery when the mains is off, although likely much less than the inverter idle current.
If a relay is going to be used in the inverter feed, and as I say I think it's best avoided, the main 100A contact would have to be closed when the mains is off. You will have a job finding a 100A N/C mains relay for a sensible price, so the way I would do it would be to use a small wall-wart power supply to operate a small N/C relay to hold its contacts open, which controls a large 12V N/O relay fed from the battery.
Advantages of the wall-wart approach are that it provides separation so you don't have to deal with mains and 12V in the same enclosure, and it provides a short hold-up time so that the relay doesn't 'glitch' the inverter on a mains transient.