Sales tax by a NY LLC but operating in NJ

Hi, I’m a TurboTax customer for several years and I appreciate it. My wife has a NY LLC that she operates one service business from in an office in New York, but she also more recently started selling items  for a different retail product business online through an e-commerce website which she packages and ships from our home in New Jersey. She runs the NJ business under a separate Doing Business As name for the NY LLC. She did it like this because we used to live in NY, and also she didn’t have to do extra paperwork and incur extra cost for another LLC. Can someone please explain how sales taxes should work for the second business because of sales made from NJ under a DBA linked to a NY LLC? We file our income taxes married filing jointly, and she’s been paying sales taxes, but I’m wondering now for sales tax for the second business operating in NJ, should she report  sales made to residents in NY and NJ to BOTH ny and nj, and she can claim

some sort of credit in her NY sales tax return for sales taxes paid in NJ? Thank you