Little help?

Hello, hoping I can get a little advice on how to best go about re-dowelling this lovely Scandinavian teak dining chair. I’m a good site carpenter but it’s a world away from fine joinery!

As you can see there is daylight between the two pieces that should be joined. Dowelling is not an issue as I’ve done a few of those when refurbishing cricket bats. What I am most in need of is a technique for getting the rest of the joints freed up so I can make the repair that is needed. It seems a bit drastic to saw though the rest of the joins. Will they tap out with a rawhide mallet or something? I can’t see a way of repairing this without breaking it a bit more :(

Hope to hear from y’all soon and hopefully I will be able to post some pictures of my repair up.

Regards,

Fez.