Oxford chair  

Try an array of nasties safely
I don't have any experience with the adhesive in the chair, but some things you might try:
For urethane adhesive: methylene chloride (solvent based paint stripper)
For epoxies: xylene or methyl ethyl ketone
For some adhesives: methyl ethyl ketone or acetone
Methylene chloride might melt the foam too. Hopefully they don't eat the wood glue in the laminate. And I can't say what they'll do to the upholstery.
And of course I think all of them will kill you fast or slow.
Any photos of the joint in question in the current state of disassembly? Maybe a visual will stimulate a more creative idea.

Glue of car windows is "cut" by sawing motion with a piano wire. Maybe the same technique can be used around the joints of armrest and seat.