It would actually be 13 ads. This is how unslotting really works. You use 5 ADs to start the process, you need 2 ADs for each card Removed, and 2 ADs to keep the Remaining weapon. You said you wanted to keep the Dopp and TG card, if you paid to have those removed you would have paid, 5+4+2=11 ADs. But you would be left with a SwXX Sherwood since you didn't pay to have the Sw card removed. If you want that card removed, you would have to pay an additional 2 ads, making the total 13 ADs. When the say 2 ADs to keep the remaining item, it means whatever the carding on the item would be after removing the cards listed.
Or did you mean you wanted to keep the D and TG card on the weapon? If so then it would only cost 9 ADs. 5 to start, 2 to remove the Sw from the weapon and 2 to keep the DTx Sherwood.