Eldiss Chatsworth 550 - 2021 model

"We thought it might be the kitchen sink waste backing up the shower waste pipe but we're not sure how that is possible."

Oh - it is!  We bought our current van just before Christmas and during our first trip away, we cooked Christmas lunch and washed up afterwards. Tipped the bowl down the sink and it all ended up in the shower.  Wonderful

It's all down to how your waste pipes are configured.  Ours were all T-d into one outlet which seems to be quite common on continental vans and therefore might not apply to yours but the T-joins were more "Y" than "T" and consequently if the van was just slightly out of level, it was possible for the water to back up if there was a sudden high volume flow. We got the dealer to re-configure the waste pipe so that the kitchen sink outlet was separate from the other two.

I'd be inclined to have a look under yours and just see how the waste pipes are joined and split them if you having anything similar to ours.

Since having had E&P hydraulic levelling fitted, I have also adjusted it to give a very slight bias in favour of the shower draining.

Your waste water 'tank' is something like a Wastemaster and is outside the van unless I am very much mistaken. You would have to be pitched on one terrific slope for the waste water to run uphill from the Wastemaster, climb the pipe and end up on your shower floor.

My conclusion is that you have an internal leak caused, probably, by the shower fitment not completely turning off. It’s near impossible to tell without seeing the plumbing layout so I guess you’ll need to get underneath and check the pipe runs and joints as an alternative cause.

Edit: Cross posted with R&R. There you are, then, a solution in the making.

Your problem could well be that there is a partial blockage somewhere along the waste pipe run. Try one of the sink/drain cleaning products, such as Mr Muscle Max Gel, and blow through using air line or blowing yourself down a piece of pipe that fits neatly into the plug holes. Don't forget to do it on all 3 sink/waste pipes. Works for me.

Another thought, is there a small leak from the shower head of pipe, or could the water be residual water that has got under the showerwall panels and is draining away slowly, after you have used the shower?

Attach some tissue to the shower head pipe and to the tap if it is wet you have found the leak area. My bet is that one of the waste water pipes has an issue and the water is taking the least route of resistance your shower drain outlet.

I forgot to add, if you go down the route of drain cleaner and a blast through, make sure that you are draining into your wastemaster or similar receptacle, as you won't want the resulting fluid blasted out all over your garden....yukkk!!😊