Hang on...
the OP says "Should add, kids love him, great dad , blah blah"
Also says she works three night shifts "so is home for half the drudge"
So isn't this the picture of a '50s household turned over where HE works and SHE just does "great Mum" ?
Now it's SHE works and he's just "great Dad"
So define work...
While she's out at work whose doing what at home?
While the OP is not there ?
Absent.
Missing.
Working.
Someone is bringing up the children.
Hmmmmm.....
Suddenly a women's work is not never done, but done exactly according to her shifts while he brings up the kids, scrubs the pots, sorts out the sports kit for tomorrow, cooks and cleans and mends and sews... and ALL that other stuff that doesn't have a pay cheque attached.
Turf him out ? Sure. Go for it. And then take on everything he's doing as well at what you are already doing yourself.
And then... (because there will be confusion about the children) get into a legal battle. And then.... cost yourself and the public purse a fortune as you bicker over every other weekend and Wednesday night staying contact. And then... as your children get older look forward to becoming the evil version (because you started it) and watch your kids learn that whatever life he is living is cooler, better and more attractive than yours. And then... well you tell me.
If you are deeply into the Protestant work ethic than hate your man (who you have had two kids with) and look deeply into a mirror. Paid work is always good but if your man suddenly found a full time job would it actually make you happy ?
You Sound like someone who likes to be OUT of the house....