How do I get to see a detailed record of all emails sent to customers,to check that they were sent to the correct people at time of sending?

It's nice to have you here, @Royangelou,

We can customize a Transaction List by Customer report to review which transactions were sent to your clients. Perform the steps below:

1. Select Reports from the left menu, and select Transaction List by Customer.
2. Tap the Customise icon button, then proceed to Rows/Columns.
   
   
3. Click the Change columns link and select Sent.

Sent transactions will show in the Sent column. Click the transaction one at a time to view the time when they are sent.

You can also check the Audit Log to view the history of your client activities in QBO. 

Please let me know if there's anything else you need help with. I'll be here to assist whenever you needed it. Have a lovely day!