Ammeter to Voltmeter...who does it?

Or I think I can skip connecting the 10ga. black wire with the fusible link to the starter relay and, instead, run it directly to the Coach/House battery charging solenoid, like the picture below. I think this will be a cleaner setup.

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Yes, there a few different ways things can be arranged.
I don't know why the arrangement you currently have uses a fuse between the two batteries. There might be a reason a fast opening device was preferred.

The voltmeter as drawn will be on full time. Probably better to have a voltmeter wired to turn on with key in Run and accessory. no?

Is it possible to have a device that regulates the charging rate of the coach battery?

One advantage of an ammeter is that is shows charging, how much and when its done. The voltmeter only shows whether the alternator is producing enough power it can potentially charge the battery(s).
If the status of the second battery is important, might be worth having a second ammeter and/or voltmeter for that system. Obviously if you did an ammeter for it, it would be best with an external shunt. The ones for marine and aircraft will probably be the best, and most expensive, as they probably must meet instrumentation certifications for those uses. But those would be a couple of places to search for info and general availability.