First of all, that 拡げられる is not a potential form. It’s the passive form of 拡げる.
Secondly, calling that 〜ている “progressive” is misleading. It describes a state that has resulted from some earlier action or change. 拡げられている describes such a state in the present, whereas 拡げられていた describes one in the past. Although I cannot tell for sure because the main clause is missing, I guess the narrator is describing a state at some time in the past.
とく (解く) is neither potential nor progressive. It is a transitive verb that means “to untie” or “to unpack”. 包み is its object here.
I think part of the reason you find this sentence hard to understand is that とく is used in the active voice while 拡げる is in the passive as we have seen above, yet those two are connected with a て-form. Since the subject is 見本, it does sound like the samples unpacked their own packages (actively) and then (passively) be spread out (to stay in the resulting state). 見本が包みをとかれて拡げられていた would have been better balanced and might have been easier to understand.
[EDIT]
(in response to added #3)
The て-form itself is timeless. There are no such things as present て-forms or past て-forms. The tense is determined by the main phrase. といて拡げる and といて拡げた differ in tense but the difference in form is limited to their endings.
A 〜ている form (which I would advise you stop calling “progressive”) can be converted into its own て-form: 〜ていて. Saying 包みをといていて拡げられている or 包みをとかれていて拡げられている is grammatically possible but it sounds very awkward. Like the tense, the aspect to be expressed by 〜ている should also be left to the main phrase.
In this particular case, I speculate the translator saw 包みをといて拡げる as one act and used 包みをといて拡げられる as its passive form as a whole. The apparent mix-up in voice can be explained by this.
I don’t like the way he put it. テーブルの上には包みをといた (or 包みをとかれた) 布地の見本が拡げられていたが would have been closer to the original (or its English translation) and easier to read.