Each entity should keep completely separate business records. This includes checking accounts.
When you commingle funds from separate business, the IRS will consider it one activity.
It should unless it is just a holding company with no transactions.
What my partner was thinking was going to happen was the S-Corp would be issuing the payroll checks but I was thinking that whatever business they are working for would be issuing the checks.
I would be more concerned with why you have the legal umbrella spanning 2 or more businesses.
The way things are set up, if you are sued in one business, you have both businesses at risk.
You also have several accounting issues. But, technically, if these businesses are under one umbrella, you could get away with having one checking account in total. Instead of separate businesses they could be separate "divisions" for record-keeping, but not for tax purposes.