Unable to rank my website - duplicate data?

Very curious about your experience in this case.
We have setup a dropshipping website with a partner.

Domain: 9 months old now (compared to 5 - 6 years of partner).

Looking into Ahrefs we have the best DR, UR, ref domains etc. However: we're using duplicate product descriptions as well as their telephone number / address for customer service (since they do that for us).

Do you guys think we aren't able to rank above them because of this duplicate data?
I'm afraid Google doesn't want to show our websites on #1 and #2 because they can see we are working together.

Very hard to exactly pinpoint the issues with your site, without having to look at the site first hand. If it has duplicate content, then yes - it will be harder (not entirely impossible), but harder to rank - you'll need to pump site authority further up, if you want duplicate content to rank on the search engine. Higher authority, higher preference to rank for something. But then there's also other factors like structured data, template coding, etc - Try using a different template that has different components - sometime a very different template can also work in favor for you.

I dont think Google will need to choose between you and your partner on who has to rank for a keyword basing on the duplicated descriptions, meaning that if there is no competition or competition is low, you will both show up in SERPs.

If the descriptions are short and represent a low amount of text percentage on the products, I dont think it will matter so much on who copied who, and will be more about overall SEO optimization. But if these descriptions are longer and more relevant on the product page, you will probable be on disadvantage against your partner almost on every scenario.

However, if you want to outrank your partner you should change these descriptions (make them better), at least on the biggest traffic urls. I dont think you will outrank your partner if you are copying his content after it has been indexed for 6 years, specially with your young domain.

There is also big chances of some more websites using your descriptions, you can check it by simply searching for the description.