Unless I am miss-understanding the issue, it does sound like Merge is probably actually the geoprocessing tool you are looking for, but you may just not be using the "Field Map" option to get the results you are after.
I would say try: open Merge tool and add all the feature classes you want to merge as input datasets. Then set the output dataset parameter to the new output feature class/shape file you want created. Next, you will adjust the settings in the "Field Map" section (this is where you will get the fields set how you are wanting). By default, it will have added all the common fields and mapped that field for each dataset, as presumably you desire. However, it will also add each unique field as you point out in your question. What you need to do is right click on each of these unique fields it has added in the Field Map section and click the Delete option. Then, at the top right of the Field Map section you should see a button with a big + in it. Click that button and specify the field properties for the field you want all the unique fields merged into (ex: if you want all the unique fields merged into a single new Text field named MergeUnique, then you would make the field name "MergeUnique", set the field type to Text with the correct field length, and such as that). Click OK to add the new field. Then, you will right click on that new field (which should show up at the bottom of the Field Map list) and select Add Input Field. In the resulting dialog box, you will select the UniqueField from the first feature class and click OK. Then, repeat this Add Input Field step for the unique field from each input feature class. Now you're ready to run it.
Note: If you spend some time getting to know the "Field Map" options, you can do some pretty powerful field manipulation with it. And the Field Map works similarly in the Append tool (assuming you have the Schema Type parameter set to No Test).