Engine damage from a oil filter not installed properly

Had a synthetic oil change done this week on my van. On way home stopped for a car wash, where I noticed some smoke or steam from under the hood, but it stopped shortly. Continued driving home and drove about 4 miles. As I approached my home I noticed a trail of smoke behind the van. I pulled up to my garage and backed away because of lots of smoke. There was a double trail of oil, and tow puddles of oil under the engine compartment. Also puddling of oil all over the engine and adjacent areas. My battery light also came on as well. I called the shop where they towed the van back, cleaned the engine and returned the van. The mechanic says the oil filter o-ring was not installed. We started the next day to take a small road trip where the battery light came on again. I called the repair shop and took it back where they tested the alternator. They said it was putting out 10 amps, and that Dodge has replaced 14,000 alternators on this make of vehicle recently. Suggested I take it to the dealer, and as I returned home the van shut off. It was towed to the dealer for repairs. So far the original mechanic is not admitting any fault for the alternator. I have pictures of the oil all over the engine, puddling and streaks of oil in my garage and driveway. Where do I stand if the dealer finds damage to the alternator or any other pieces or parts to my engine? We have a big road trip planned in a week to the east coast. Should I be worried about this? Appreciate any help. Thanks.