As far as I know the officials at the MX border have to be the ones to remove the sticker - they have to see the vehicle and see the sticker on the vehicle and see the sticker come off. Reason being - anyone could take the sticker off and return it but leave the vehicle somewhere in MX. I have heard of people doing it by returning just the sticker but it is a real hassle of paperwork.
Depends on what part of NM and AZ you will be in. Way over south of Deming, NM we have crossed at Columbus/Palomas where the officials are right at the border - within a few feet - and there is a large parking area on the US side. You could walk to the office and ask them there. Be aware that even though it is only a few feet you still have to return through US customs and have your passport. There is no easy place to park an RV on the MX side but it can be done. We used to cross there to go to dentist and eye glass place - and when fuel was still cheap we would drive 3 blocks to the Pemex to fuel up and then just turn around and return to the US. We talked to the US officials first to make sure what we were doing was OK with them. Now fuel is cheaper in the US so no point to that idea.
