For whatever it's worth, I personally would not trust
anyone to put the correct coolant in an LX/LD Dodge or Chrysler. This is less common today, but ever since Chrysler switched from HOAT to OAT coolant in 2013, I've found that very few mechanics seem to know the difference, and from what I've seen, it's not unusual for even ASE Master mechanics to mix them up. Since they're not compatible and mixing them can cause sludge to form and clog your cooling system, I do it myself.
If you're going to let the stealership do the work, make sure they give you a detailed invoice with the part number for the coolant, and if possible, make sure the bottle says "10 years/150,000 miles".
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I am like you mate with the "not trust anyone".
I haven't really dealt with many dealers (enough stories with people from dealers who have), but even if you "make them make a note" - every time I have seen that they ALWAYS ignore it and do "yeah, but we always......." The Hyundai dealer near my Dad are a shocker, untold problems with two of his cars (one a bought from new one) because they have no idea, and just will NOT listen to customer. Granted, most of their customers have no idea; but when they get one who DOES; they actually resent it/argue. Maybe because you will catch them out, as their knowledge is VERY shallow. With two cars they diagnosed a fault, I took it home and fixed it. Not what they said/they were incapable of fixing it.
I know is totally different car, but shows the mentality. I have a Triumph Stag with alloy (aluminium) wheel nuts. They do up tight, but NOT with a rattle gun, by hand only to same as my 300 (100 ft/lbs).
Had for 30 years. First time I got tyres, I took it in and said I would only get them there if they used a wheel brace and NOT a rattle gun. Small town shop, but one of our largest tyre chains, so they did. I explained to him they were alloy, MADE him write "Must use wheel brace, NOT rattle gun" on ticket.
Guy gets ticket, looks at tyre size, throws ticket aside, grabs rattle gun. I said "You can't use that". He says "Oh, I always do". I say read ticket, he does, "Oh, well, we don't have a wheel brace......." I hand him mine "Oh, we can't use customers tools, so....." and starts with the "We do ALL kinds of cars here mate, BMW/Porsche....." in other words, he was adamant he would NOT do it other than rattle gun.
I say take it off the hoist, he's not doing it then. Manager comes out; tells the guy to go and get wheel brace (they had one, he just didn't want to) and NOT use rattle gun. He removes wheel nut - "Gee they are light, aren't they???" He had NEVER seen alloy wheel nuts before, but that didn't stop him trying to strip them. Mate of mine had an MR2, got new Italian wheels. Ordered them in for him, and stripped every wheel nut. He had to put old ones back on/wait for new set of nuts to be ordered in (alloy). Again, he MADE them make a note they were alloy/take care = totally ignored it, did what "they always do/I know how.........
So I take the Stag wheels in now in another car, don't let them touch the fitting to the car. They WILL NOT listen/read the "little note" on the tag.
Hence I am very careful with anything with dealers. They think they are "so professional, don't need to listen/check etc.
If there is a possibility they can stuff it up, chances are..............................