Wherever you are comfortable and at ease with yourself is your home, regardless where you were born or brought up.('Home is where you lay your head' and 'Home is where you hang your hat' are also used.)
Someone who rules or controls something with an iron fist is in absolute control and tolerates no dissent. An iron fist in a velvet glove is used to describe someone who appears soft on the outside, but underneath is very hard.
'Mailed fist' is an alternative form.
If the left hand doesn't know what the right hand is doing, then communication within a company, organisation, group, etc, is so bad that people don't know what the others are doing.