Remove 100 yr old glue
First to refinish, unless the joints have failed DO NOT take it apart. Also you need to know how the chair was manufactured...is it just mortise and tennion...are the mortise thru drilled and the tennion wedged...are the tennions blind wedged (fox tennions)
What style of chair is it?? If it is a Windsor chair they are ment to be painted as the used differnt woods in the manufacture
If you are set on taking it appart....
Get a syringe, fill it with HOT water and squirt it in the joint...wipe off excess water, and warm with a hair dryer.
Bring a tea kettle to boil and hold the joints over the steam....be careful not to burn yourself.
Again unless the joints have failed DO NOT take it apart. Even if they have failed you are better off to spread the joints and inject more warm hide glue.