I was watching a "Chibi Maruko Chan" episode about Maruko wanting to pet a fluffy dog. In the subtitles, I saw「ずっと触ってたくなるよね」. So I understand that ずっと means "continuously," and that さわって is the te-form of 触る. What I don't understand is what たくなるよね means. At first, I thought that たくなる was たい (En: want) conjugated to たく when なる (En: become) is attached. However, たい is typically attached to the masu-stem of the verb, not the te-form. This is where the confusion arises. An explanation for this construction would be much appreciated. Onegaishimasu!
As you guessed in your comment, ～てたくなる is a form of ～ていたくなる. (I wouldn't call it an error, though. This is a very common colloquial pronunciation.) It is not a shortened form of したくなる, because したくなる cannot even fit in these sentences to begin with.
～ていたくなる is form of ～ていたい, which is itself a form of ～ている. As ～ていたい means 'want to ～ている', ～ていたくなる means 'become wanting to ～ている'. With your example, ずっと触っていたくなる would mean '[If I pet it], I'd want to be petting it for ever'.