There's no easy answer to one aspect of this:
Many DV victims are panicked at the thought of their ex doing something to them (usually it's a valid fear), and are looking for any type of security they can get. The problem is that many (by no means all) do not have the proper mindset for, let alone training in, the usage of a weapon. Yes, yes, this is the same Anti line used to object to CCW permits in general, but consider one thing; a CCW applicant has self-selected him/herself for the CCW license because he/she has an interest in the usage of deadly force for self defense. In the case of a DV victim, this is less likely to be a calm, rational decision made before a threat has materialized, and more likely to be one made out of fear.
This may or may not be a valid reason for opposing this bill (the RKBA advocate in me says it is not), but it remains an uncomfortable fact. I have, personally, seen a lot of battered wives say "I need to get a gun, he's gonna kill me" and admit freely that they know nothing about self-defense laws, to say nothing of sound tactics or mindset. When the threat is looming is not the appropriate time to be preparing for a fight- this is a decision that should have (and in the case of the CCW permit holder, has) been made a long time beforehand.
Mike