(((hugs))) honey. You must be reeling from the shock of losing your dm so quickly 
It is a recognised fact that grief can make people behave in ways that may seem completely out of character for them.
My guess is that your df is shellshocked by the speed at which his dw fell victim to the bastard disease that is cancer, and this has caused him to confront his own mortality.
In taking up with a ladyfriend who's had a 'shit life', I suspect that he's using her sad but markedly different circumstances to reaffirm that he's a 'vital' being in that blood is still coursing through his veins, and that he's still 'needed' by a woman.
It may also be that in telling your db that he 'has a girlfriend' your df is attempting to take some of the pressure off his family; signifying that they don't need to worry about him being lonely or being burden on them, which is something that becomes of increasing concern to us the older we get.
It may simply be that your df is in denial but, regardless of whether anyone considers it disrespectful for him to even think about having any romantic inclination towards a member of the opposite sex so soon after his dw's passing, the truth is that he isn't hurting your dm in any way and every memory that everyone who knew and loved her has of her remains intact.
I've got a feeling that your dm's smiling benignly down on her dh and saying 'enjoy yourself while you can, you silly old sod - I'll have your guts for garters once you get over here' 
FWIW I thought twice about adding the grin emoticon but felt compelled to add it to indicate that your dm isn't at all offended by this turn of events and she wouldn't want you to be perturbed either.
Here's to your dm 
and her robust sense of humour - she's not lost that.