Hello bcr_garrett,
I have read your issue and it is one about timing and they can always be a little tricky.
First, when you Clear Screen For New Entry, you take away the information off the screen and it can not be used. On the other hand, it shouldn't affect the refreshing of the page. It looks like you have the refresh grid/information command in the wrong spot. I'm going to recommend using a popup to update the information. Here is how.
1) Have a button to click that opens a popup displaying customer information from another table. The button would have a 'Show Screen In Pop Up' Action set with the screen of the Child table.
2) To close the popup screen, have a button with a 'Close Pop Up Screen' action.
3) Here is what I believe you are missing. In your parent screen, click on 'Advanced…'. In Step 2 of 5: Actions, create a new Event for 'onClosePopUp'. (The default is OnScreenLoad and hides the other Event options). Create a 'Refresh Grid' action for the parent grid you are looking to have refreshed automatically. You can try your clear command here.
Please let me know if this helps or you need more clarification.