You're entitled to it. Do what you need to do to get it.
If you're worried about the timing, can you have your new job start a little later?
I'm sure that while they'll be disappointed to have you leave, your current employer knows your value and won't want to burn bridges with you either. At least if they have any sense...
Bottom line: You have no control over how they react. You've held up your end of the bargain. Do what's best for you. If they react poorly, then they likely would have reacted poorly in some other circumstance if you stayed.
Luck!
Cheers,
Scott.