Did you complete your inverter installation... inquiring minds want to know
Kind of, read on
I believe your problem lies in that you are draining off the larger buffer battery with your house inverter. It is best to have the batteries sized the same if you are going to parallel batteries. You need the bigger battery as the first battery off the HV car 12 volt battery charger and your buffer (if used) should be the same size. If you are determined to use the smaller battery it needs to be the one that is at the end next to your house inverter but is still not ideal and I don't recommend it.
Using the smaller battery as the pass through (as you are doing) will not force the onboard car charger to see the larger low charged volume battery at the end that your home inverter is sucking from. The larger volume battery at your inverter end will only slowly equalize from the smaller volume battery.
Doing it with small battery sandwiched between the HV and buffer battery will have a slinky like effect. Just add a larger battery (preferably lithium) to your car and the onboard car charger should keep up. If you feel it won't because of your possible load then add a buffer battery of the same size and type. You will not get the slinky effect if you hook your positive cable to opposite end of your paralleled (banked) (same sized) batteries from your negative cable.
I run mine without a second battery. My 12 volt is lithium and it runs a 2000 watt.
Good luck and tell us how it goes.
Ok, so I hear and understand everything you're saying but it seems that model3 is clearly limiting the charge going to the buffer 12V battery. From what you're saying, I should just be able to drain 10A from it with a small inverter, and it should get topped off quickly enough, but it seems that on model3, the charging speed is limited, and it recharges more slowly as it discharges.
As for "The larger volume battery at your inverter end will only slowly equalize from the smaller volume battery". That is not correct. If the cable between them is thick enough, amps will flow from both batteries as regulated by their internal resistance, and any imbalance between them will quickly resolve itself as long as the wire between them is thick. I know that because I have another system with a big and small battery and as long as I equalize them before connecting them the first time, they stay at the same voltage forever after that regardless of what I draw from them.
Back to what I had to do: I thought it would be as simple as plugging the big inverter directly into the 12V connection from the DC-DC converter, but I found the following:
1) unscrewing the bolt to the 12V + connection point gets it to disconnect just enough that the car can sense amps aren't flowing as well and can get upset with error messages. It's better to find a right size bolt, and add the second connector on top without disturbing the first one.
2) the converter is sensitive to high amps. Inverters have a huge capacitor and draw enough amps when you connect them to make a big ass spark. When that happens, enough amps are drawn that the DC-DC inverter shuts off. When it does, it shows 1.3V and does not turn back on easily, or at all.
Once you're in that state, this is bad because your buffer 12V battery does not get recharged and starts draining until it's empty. Once, it reset itself on its own, and another time, it did not and I had to feed 12V to the external battery so it didn't go flat
3) I haven't figured all the ways the DC-DC converter can turn itself back on, but eventually found that if you disconnect the + from the buffer battery while the DC-DC converter is shut down, then the entire car has no power, and shuts off for good. Once you connect the battery back, the DC-DC converter turns back on and everything comes back to normal
4) well, almost, if your 12V battery is too low, the car tells you it needs to be replaced and somehow fails to charge it to a suitable level, even after 24H. I had to unplug it, use an external charger to bring it back to 13.5V, and now everything is back to normal. This further confirms that the model3 battery charger is weak and/or limited
5) I now have a careful method to power on my inverter using a resistor to limit current when it equalizes and then connect the full bypass cable once that's done. This is error prone though and may need to be repeated each time the inverter shuts off after the DC-DC inverter turns off for whatever reason. However, once it's up and running, it ran my fridge for hours without issues.
I haven't solved the current inrush problem yet, but I'm thinking about using a zener diode across the inverter connections that will control a bypass relay that allows a full connection to the inverter, bypassing the current limiting resistor. The diode will only allow current flow to the relay once enough equalizing has been done through the resistor.
That will take a bit of time to build, but I'm reasonably certain it will work.