OK, so the trick to that is to create a new field in your data entry table which is a formula text field (assuming that your code is a text field, otherwise numeric), and make the formula simply be the code field that you want to enter. Then once again delete the relationship but this time build it on the formula field. So to be clear, a data entry field, and then a text formula field equal to it and build the relationship on that formula field.
So, the effect of this is that you are not "directly' entering the key to connect the tables and hence you will not be put into the record picker which most users hate. The description will certainly pull in when you save. If you have that formula field on your form (even if its hidden by a form rule which causes it to be always hidden) then it will probably pull in during order entry after you tab out of that data entry field and the formula calculates the value of the link field to the relationship.
