Too many people with an opinion! I have qualifications in electronics and electrics and agree with you.
My battery has been on charge for 3 years now!! Use for lighting and water pump.
The easiest way would be, as you suggest, to use a small inverter. Look at the ratings labels on your chargers and choose an inverter with a higher rating.
Not sure about the vacuum cleaner, may be quite power hungry, again check it's ratings label.