I am just not sure how to create a new related record without going to the layout.
While you can write a script to interact with your portal to create the related record, going to the layout for that table is simpler and more flexible. You can use freeze window to freeze the window, go to the layout for Price Adjustment, create the record and then return to the original layout. The user just sees the new data appear. What ever value you are using to link Transaction to Price Adjustment gets stored in a variable so that you can assign it to the appropriate field in the new record that you create on the other layout.