Tim Inman: The two best enemies of hide glue are heat and moisture. Use them to your advantage. I usually prefer steam when I'm needing to release a tightly bound hide glue joint, assuming there is a reason justifying the release. Alcohol can work, too. I prefer steam. But, probably the reason that oak top is only "partially separated" is that the wood has shrunk and changed over the years, pulling apart the ends. In that event, I would recommend you consider either filling the open end with an appropriate material, or recutting the joint so it fits right again. "Why did this glue fail?" is a question we must always ask and answer in good restoration work.

Chris Marshall: If you do cut the joint apart, I'd also give the wood a few days rest in the shop -- especially if the split glue joint is only a board or two from the edge. If there's any tension in the offcut piece, it might distort a little more. Then joint the mating edges flat before re-gluing, just as though you are making a new butt joint. I'd go with hide glue again for making the repair joint -- after all, it's lasted this long!