Usually a shore charger
and laternaotr co-exist very nicely since only one or the other is "talking" and charging the batteries at any given time. In theory each one has a voltage sense lead that tells it the voltage level at the battery and there's no conflict since only one is working at any time. Usually.
If both were running at the same time, the question becomes which one is really putting out power? And what is the voltage sense lead really detecting, battery level or the power from the other device? And that's where the problem can come with solar, if the solar panels
are putting out power, unregulated, it is often higher than battery voltage.
If the batteries are depleted and really soaking up all they can, they'll eat up that extra voltage and the voltage sense lead from your alternator
(or shore charger) will still get a reasonably accurate reading. As they get nearer a full charge...the voltage sense lead can't tell the difference between the voltage coming form the solar panel, and the voltage in the battery, so there's no way to predict whether it will reduce the output (from the alternator or the charger) too much and just waste your charging time.
Far simpler to add a 2-way switch, and leave the solar panel connected for maintenance
charging on the hook, while using JUST the alternator or charger at other times.
If your solar panel is only putting out a small charge (i.e., "trickle" chrging) then it needs no controller, the battery can tolerate a certain amount of uncontrolled charging. If the solar panel puts out a relatively high charge rate, you'd be better off with a charge controller on it. Since AGMs can be killed by overcharging, you might want to check the maker's specs to see just how much of an uncontrolled charge they can take without damage. Or, just get the controller to be on the safe side.
"My reefer drains into the bilge. " That's nasty either way. You might consider putting a blivet in the bilge, most restaurants and diners will gladly give you an empty five gallon "mlik bag" from their milk machines, once rinsed out if makes a good way to trap and store five gallons of drain water that you can pour out manually when you get aboard. Or of course you can spend a lot more to buy a Nauta bladder.<G>