Hooking ice maker up to bottled water.

Filter the water into the coach.
The filters sold by CW and Lowes even are not the end all.
We have a CW filter, don't remember the name but 30.00+ and Lowes GE filter that will filter down to .5 micron and has silver in the charcoal.
They will get iron and sulfur and lead and a bunch of other nasties.
They will even take a bunch of lime. Much of the lime in water is large enough pieces to be seen in a clear glass of water. It will get that but not dissolved lime.
We have a couple of the ceramic filters, that were available at CW. They filter down .9 micron. The water on one campground went through the other filter above and still the ceramic caught a bunch of sulfur.
It took quite a bit of scrubbing but the filter was eventually cleaned.
An under counter filter down .2 micron will filter the water to your fridge quite well. There should be a shut off valve and fitting to the tube to your refrigerator there. An undercounter filter should serve both.

I think you might need to hook up a bottled water dispenser to a dedicated water pump feeding the icemaker. While you are at it, hook up a drinking water tap. If it is an ice maker in a refrigerator, gravity fill won't work, the device is expecting more pressure.

There are portable ice makers that are gravity fill. I find it easier to fill ice cube trays from my RO purified drinking water supply, put them in the freezer. Got into that habit when I lived where RO purified was the only safe water source for drinking, unless you boiled, and even then the tap water had an oily taste. Every home, every office had a dispenser.

Ice makers, water chillers in a fridge are usable if you find the water drinkable after whatever treatment you apply. Easier to do at home, where the supply is more predictable and you know just what you have to filter out, physically or chemically.

Why not put a filter on it...? There are tons of options for RV water filters out there.

Buy some ice cube trays from Bed/Bath & Beyond and fill them up with bottled water ... place them in the freezer.
Otherwise ... your ice maker water supply needs to be pressurized.