Want a happy end to Mirai Nikki? Then WATCH THIS.
Really, it's simple as that. If you felt unsatisfied with the ending of Mirai Nikki, with the way they had to part ways and basically still not being allowed to happily live together even after all they've been through, then watch this OVA.
Of course, it gets creative at some point to pull it off, but come on, we're talking about timelines, timetravel and future telling here. You can't say "no, this is not possible!" at many things.
Most things in Mirai Nikki as well as in this OVA can be based on valid theories of time (like memory dripping through interference with different timeline versions of yourself).
But even if you want to be more critical about how it plays out, I feel you could easily overlook it for the sake of their happy end. It was satisfying.