.............If it's simply a repair job, use the strong modern product. When I repair I 'fix it good' so hopefully nobody will battle with my techniques, cos it's not gonna break again! ......
Best o luck Henniep, but I suspect a goodly number of such repairs will fail again in due course because it isn't the glue that's the problem, it's the design or construction of the chair that's the real issue. I constantly read that folks use "strong modern glues", with the implication that hide glue is less "strong". In a well-made joint, hide glue is stronger than the wood and forms as good a bond with the substrate as any synthetic glue. In fact it is "stronger" than many PVA type glues and does not "creep" so (if used according to directions!) is a better choice for any joint subject to prolonged loading. Its main failings are that it is not as convenient to use as "modern" glues (more fuss getting it ready short open times & poor joint strength if overheated or not fresh). However, it still has it's place in many aspects of woodworking. Horses for courses - I use PVA or epoxy where convenienceor other factors are important, but HG is my choice for any piece I expect to last a generation or three. As many have pointed out, its reversability is both a weakness & a strength.
Getting back to chairs, most failures on Windsor style chairs occur in the rungs or "stretchers" because they were made with little or no understanding of the purpose of the stretcher. These should put enough outward pressure on the legs so that when sat on, there is little or no extra tension on the joints (ever wondered why they're called "stretchers"?). A well-made Windsor needs no glue at all on the undercarriage and if the legs are through-tenoned into a thick seat it doesn't even need stretchers. I've sat on such chairs that were >100 years old that were as sound as a bell.
Take a good look at the next chair you have to repair and you'll most likely see that the vast majority of the joints that failed were in tension under load or subjected to severe wracking stress and the joints are simply not structurally up to the job. The actual glued area on dowels is small, & half of it is typically against end-grain. No matter what glue you use, there is a 99% chance your repairs will fail again sooner or later. I "fix" them for folks, but like Jacob, I know my efforts will most likely be in vain.....
Cheers,