The achievement (coat of arms) that you attached isn't a Douglas coat of arms as far as I can ascertain.
The top left hand corner (dexter chief) is the 'surname' part of the arms and there certainly aren't any Douglas arms that look like that. However, in the 2nd quarter there is something similar to the Douglas arms but without the imperial crown, so it might be a wife from a cadet branch of one of the Douglas families.
For arms in the name of Douglas, the Douglas arms would have to be in the dexter chief quarter. The Douglas arms are Argent a Man's Heart Gules ensigned with an Imperial Crown proper on a Chief Azure three Mullets Argent. There are also other arms registered in the surname of Douglas, but none of them look like the image that you have provided.
If you want verifiable facts on these arms I suggest that you take your enquiry to the Office of the Lord Lyon for that is where they MIGHT have emanated. m You can 'Google' for the address of the Lord Lyon's Office or you can get the info from http://www.lyon-court.com
If you do take your enquiry there, please let us know the outcome.