Give them two weeks notice, but make it clear you would appreciate any chance to leave sooner if that is OK with them. If they agree with you that you're not doing great at the job, they'll let you go on your way immediately, before the two weeks. If they don't agree, and they think they need you, then you have to stick it out for two weeks, but you at least won't put a bad mark on your career by having left with no notice.

And you don't say anything about the nature of the personal issues, so it's hard to say more. But they might be able to help with those in ways you don't realize.