Re: OOC
No, you can only ever add your Proficiency bonus once per die roll, no matter how many ways it might apply. That's the General Rule.
On the other hand, and it just may be me, but I don't see how you could be proficient with a set of tools without also being proficient in the skill that uses them, which seems redundant. If you were proficient with Thieves' Tools, wouldn't that make you proficient at picking locks and disarming traps as well, since how else would you have acquired your proficiency?
So, a Soldier who wants to pick a lock is proficient with Thieves' Tools (how did he get that?) but isn't proficient with the lockpicking skill gets the proficiency bonus.
In any case, one of your cover identities should be Locksmith so that you can claim the Thieves' Tools you are carrying AREN'T in fact Thieves' Tools but 'Locksmith Tools'.
Maybe you went to Locksmith Camp as a kid!