There may be principled objections to the idea behind the Violence Against Women Act -- for example, the assumption it makes that women need to be under the special protection of the Federal government. It's clear that Maid Marian benefited from her status as a royal ward, but it's not equally clear that all women ought therefore to aspire to an equivalent status. Nevertheless, in politics as in war, there are times for digging in and dying in place if necessary; and there are times to recognize that you've been outmaneuvered, and preserve your forces for another day.
In this case, though, the Republicans seem to be doing neither the principled thing nor the smart thing. This is largely a re-approval of a bill that passed with broad bipartisan support before, so it's not clear that the Republicans do have any strong principle at work as a party here. This isn't a TEA Party stand against the idea of women as wards of the state; the party leadership is wholly OK with the VAWA, except for a couple of changes in the re-approval.
So, it isn't principle; and as for smarts, those changes (as Mother Jones points out) were made last year. Good job picking your moment.
Those changes do touch on hot-button issues. Nevertheless, one of these policies is totally reasonable if you buy the VAWA as a general principle: while there are very good reasons to oppose the idea that lesbian relationships can constitute a marriage, there are no reasons to oppose the factually obvious reality that they can be violent. If you believe that VAWA is an appropriate solution to violence against women, then there's no reason it shouldn't hold for lesbian women as for unmarried girlfriends of bad men.
One certainly could oppose the immigration-visa change, but by itself it's not worth the price of the fight. It would be wiser to let this one go; there will be better ground for re-fighting that issue on another day.