I'll go ahead and answer because I think your core question is a good one. It sounds like what your company installs are fairly complex home automation systems, and you're hiring residential electricians to do the wiring. Instead, what you need for applications like this is an electrician with industrial automation experience. They do exactly the type of thing you're asking all day long -- wiring rack-mounted PLCs and relays, labeling wires according to ID numbers on a diagram, high voltage and low voltage wiring and termination.
Another thing you need is a contract. If having your circuits and wires marked a certain way is important to you, then you need to specify that in your contract. You can't just assume that your electrician will know that you prefer ID numbers on your circuits just because he has a sheet with ID numbers on it, especially a residential electrician whose usual clients would have no idea what the ID numbers meant. And then, if something isn't done according to what you spelled out in the contract, you can point it out and the electrician will correct it. The other stories you mention just sound like mistakes that should have been corrected by the electrician, assuming they were his error (was it you or he that ordered the relay panel that didn't have enough room for 200 wires?). Anyway, everyone makes mistakes now and then.
To answer your specific question, there already is a system for diagramming electrical circuits. You should probably already be familiar with these symbols if you're installing home automation.
One last piece of advice for good communication with your electrician if you're working in the U.S. (which you may not be): make sure that what you're calling these devices matches up with U.S. terminology for these devices. For example, in the US, you would never call a switch with an "up" and "down" position a pushbutton. Here, a pushbutton is a button that you push into the surface on which it's mounted. Up/down switches are normally just called switches, at least in a house. I don't know what a wallet is, maybe a wall outlet? And it would be very unusual to have a 220V lamp circuit.
It sounds like your plan will work now that you have the 12/3 cable -- since you have a neutral at the kitchen-side switch, you don't need to worry about running one to the entry-side switch, as the 404.2(C) provisions for neutral at switches only require neutral at one location within a multiway switching setup.
Best Answer
I Normally draw a rectangular box and provide the room dimensions. Show the location of the door and the light switch. In the diagram show where the feed is to the existing light or the switch and the location of the existing fixture with wire running from the switch to the fixture.
At each location you draw the cables list the size and /type and or conduit examples : 12-2WG or 14-2WG for Romex. If conduit 1/2” emt 3 ea #12 thhn or possibly MC 14-2 WG (Emt electric metal tubing, MC metal clad,)
I usually change colors and show the new fixtures fed from (the original light fixture box or switch). If any question of box fill I show the Fill calculation for the size and type and box size if only 1 in 1 out I don’t
switch loops fed from the fixture I do unless the box is separate. the fixtures do not have to be exact locations the wire route is approximate. I have turned the drawing in on the hamburger wrapper from my lunch in one case but they usually like it on an 8-1/2 x 11 paper your name and address the location of the room in the home with an explanation like “existing feeder 14-3 nmb (Romex) from main panel 15 amp breaker #6 . Addition of 3 ea ic can lights 60w max.
I have never had to provide more than this and as I said I have laid out a quick job for a guy that caught me in town and I drew it up on a hamburger wrapper it might have been yellow and the inspector told me I better have a burger for him on the inspection. But approved the drawing and gave me the permit on the spot after copying it.