No, no typo. My problem is that the first garage who looked at it and charged you (can't believe they did that) have not fully identified the problem part. So you might end up paying for a motor, a loom and a resistor. Even a half decent warranty company would not pay for all that and would demand a proper diagnosis. My experience of dealers is that they will always want to do their own check first. As yours is a failure on one of their cars they should put this right at no cost whatever, parts or diagnostics.
Sounds as though the manager needs to learn some management skills. Have you tried the dealer's head office for example? Have they got a customer service department?