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Is the insurance company looking after this? No it is not normal at all and I'm surprised the alignment shop would even allow you to leave like that. That really does put them in the Legal Loop for sure if they did.
Can you post a picture or two of what your talking about? Either way, I would get a another opinion on this (but that will be your choice if you do or not). I wouldn't drive it anymore than you have to (if at all) and definitely not highway speeds.
Is their a government agency in your area you can call or get them to look at it for you? This is the route I was going to take when I had my front end hit by person who was towing a tandem trailer behind him, he cut the corner to sharp where I was sitting and he hit my left front wheel and almost took it right off. When I got it back from the auto body shop that looked after the insurance claim and alignment it was way off.
When I found out where the body shop took the vehicle for the front end work, I called them and he told me he was instructed to only do a Tow In on it?? I then asked him if he knew how dangerous that was and legal ramifications he would be facing if something happened. He refused to do anything about it. I said fine, and told him I would be taking the vehicle to a friend of mine that does Commercial Vehicle and Accident Inspections (causing death) for a local police department and if he found anything wrong or "BuckSheed" back to together, that I would let him do the follow up.
Needless to say, he insisted that I didn't do that, and to bring it back to them and they would make sure everything was safe (which it turned out to be no where near safe). 2 days later, I got my van back and everything was just the way it was before the accident. I told the Auto Body shop and the Alignment shop what I thought, and also told them I carried a Special Needs child in the vehicle on the weekends (at the time) and did alot of highway driving with her in it.
This was a body shop that had a very good reputation in the Burnaby area that instructed the alignment shop to just do the tow in, the lady at the body shop was very friendly, but the guy was very Cocky and Arrogant and he was the one that instructed the alignment shop to do this. After I told him what I thought about his "Cut Corners" workmanship and that I would be filing a complaint against them on such a dangerous decision he chose to make, he got all real "Pretty Friendly" at that point and apologized for such a stupid mistake, I accepted it, and moved on. I will never take anything to them again and I will never recommend them again either because of it.
I know some people may think I'm a trouble maker and give everyone a bad name for no reason, not the case at all, I'm very easy going overall and I always give the shop an opportunity to make things right first. I don't do this kind of work and I don't expect this kind of work to be done on "my" vehicle, If it is, and they refuse to correct it, then you just pulled on the "Monkeys Chain" and watch out, because he's coming down from the trees with hands and feet fly'n . Just to much of this going on these days, I see it all the time at the shop when customers bring their vehicles in with a problem another shop made and refused to correct it.
Something to consider and definitely get a another opinion that has some pull in you favor with this. Hope this helps. Please keep us updated, I'm curious now on the outcome. Thanks martyroy.