Definitely a non English speaker. We wouldn't even say anything remotely like this. Probably from Hong Kong.

I do not find this so strange. The thing you should fix is "in business." I know you are talking to a business partner, but the purpose of the letter is to seem friendly- not to prove you want their business. You seem friendly, then in return you may get business. So... Because we have not spoken recently, I thought I would send a message to you. We trust that you are doing well, and look forward to working with you agin as you see fit. My best to you and from all of us at_____.

I think it sounds Chinese. But if you choose to use Jesse's version, make sure you say "again," not "agin."

"We trust" in this context has the sense of "we hope" or "we are sure that", it's a complimentary phrase that shows a personal touch. I wouldn't say that I find it strange at all. I would write, in example, in a professional email "I trust this message finds you well" = i.e. that I hope that they are well when reading this message.