Fairenuff - that's really good advice. What should one do if any of the rules get broken though?
You stop the discussion and wait until you are both calm and then you talk about why the rule got broken - did someone lose their temper and swear? If so, they should apologise and agree to not do it again.
It takes time, you need to keep trying but don't flog a dead horse. He has to want it as much as you do.
Basically, you love each other so you should be kind to each other, not try to hurt or score points. You can accept each other's failings, provided that they hurt no-one.
Remember this. Every adult can control what they say (sn aside). We should not be rude, dismissive or aggressive to our loved ones just because we think they will excuse or accept it. We wouldn't talk to strangers like that, or our work colleagues, so we can control it.
How we talk to each other is a choice. Sometimes it is learned behaviour from our parents but we can change this.
We both work full time but the default position is that childcare and housework are my remit.
This needs to change. You should sit down together and make a list of absolutely everything that needs to be done to run a house. Making the list could take some time as it's surprising how much there is, from the house to the garden, the car and the children, insurances, paying taxes, researching holidays, etc. When you have the list, take it in turns to veto the jobs that you absolutely hate doing. If neither of you is happy to do it, you will have to find a way to pay someone else to do it.
So maybe you mow the lawn and he weeds, or you pay a gardener. You clean the bathrooms, he cleans the cooker, or you pay someone to do both. That sort of thing. Regarding childcare, don't forget to take turns doing the night shift if the children still wake, or if they are ill.
Try and free up enough time so that you each get equal 1) time to yourself, childfree, to do what you want 2) time as a couple, childfree to do something you both enjoy, and 3) time together as a family to do something the children will enjoy.