Your translation is correct, and どんな意味が込められているのか考えるもの(=形) is a completely natural Japanese phrase at the same time. Grammatically speaking, I think this is something called a gapless relative clause explained here. Other similar examples include:
英語を学ぶ楽しみ the joy of learning English (not "the joy which is learning English")
カエルが水に飛び込む音 the sound of a frog ...
Your translation is 100% spot on.
However, this usage of 考える is neither colloquial nor poor use of the language.
Following your same logic, パッと見て何を模したかわかる形 would imply that the 形 is the thing doing the looking and the understanding, but we know that to not be the case. We know that the thing doing the looking and understanding is a general person, the '...
This 'の' should most naturally be regarded as an apposition, rather than possession. So it refers to a 姉さん, who is your 親戚.
Looking up a dictionary, the definition of the word 姉さん usually starts with these two:
older sister (広辞苑: >「あね」の軽い尊敬語…)
young lady (広辞苑: > 若い女性を呼ぶ称。)
In the phrase 親戚の姉さん, it falls somewhat in between. I think "a female, comparative ...