I think the agreed rules are less important than agreeing with dw that a united front is very very important.
No wonder things are calmer when you aren't there - that is how it could be all the time with you there or not, because things will be calmer when there is only one set of rules - it isn't you that is the problem it is the dual rules which are in play and which cause this whole pingpong situation with DS going to whoever it suits and conflict ensuing while resolution between the alternatives is sought in the form of a three-way argument.
Personally, I think that DW is being very short sighted if she thinks providing an alternative set of rules from you is a good idea as kids know how to exploit it and both of you will need all the authority you can get now and as DS grows up.
Any split in the camp undermines the authority of you both and can only store up trouble.
I think you need to strip back the discussion, forget about the specific rules for a minute and discuss why you think a united front from you both is absolutely critical. If you and she can agree that being on the same team and not giving ds mixed messages is the most important thing that is the first step, then if you both believe in that, then you can decide the individual rules and find a compromise you are both happy with and will both enforce, and then, only then, does the DS get to know what the rule is and finds both of you backing it up.
You have to agree to agree with each other in front of DS, despite the fact you have slightly different approaches. The fact that you have slightly different parenting styles means that some discussion will have to occur before the final mutual decision is put to the DS.
Of course you had discussed and agreed this rule you talk about, but if you aren't both seeing that a united front is key, then this re-nogotiation in the heat of the moment will keep re-occurring.
It is so undermining to have to haggle out what is or isn't OK in front of a child. because in order to have willing obedience the child must not be thinking that this rule is essentially fluid or arguable.
What does your DW think about the principle of a united front? She clearly didn't really believe in the 'no electrics before breakfast rule' even though she agreed to it. She perhaps agreed, but on the spot in the face of child resistance, doesn't actually believe enough in the higher principle of backing each other up enough to have put her foot down about it.
I think your DW is causing the disturbance but it looks like you because all is calm when you aren't there. But you can't be in a position where your DW is the only person who enforces anything your DS needs to know he has to listen to both of you. But that won't happen if he can just look to his mum to get him off the hook. :(