You are not alone, unmumsnetty hugs and sympathy here!
It’s rubbish. You’ve just had surgery. You try so hard to manage everything no wonder it’s all come to a head. Don’t blame yourself.
Have you tried talking to someone? Even the Samaritans- it can help just to speak to someone and “offload” without there being any negative responses, just a listening ear.
When you go home, get the kettle on a table with some coffee and spoons, cups, even powdered or long life milk if needs be, next to where you sit or sleep, so you can at least have a cuppa easily.
The kids will either be avoidant, or arsey, or shamefaced. Under it all they are also probably worried, scared or upset (even if only for themselves!!!) they don’t even know how to deal with their own feelings let alone the whole situation.
Maybe the house will be messy for a few weeks, it doesn’t mean it will be like that forever. You’re really ill right now, so right now that’s not a priority. You are. Your health is. Put housework in the “fuck-it” bucket for a few days!
The work thing sucks but applying for jobs is probably a bit beyond you for a week or so. Go home, take the weekend “off” worrying and do something to distract from the worries, even if that’s reading, a stupid online game, listening to your favourite album from your youth...