Hi Julian, What type of glue did you use?
As you are using spotted gum, I guess you are in Australia? If so the best glue locally available is techniglue an epoxy, which is much stronger than hardware store quality stuff. It is available from Carbatec specialty wood stores.
If the splice has come apart totally you can, soak it for a couple of days in an old tin filled with acetone, this will dissolve the previous glue. You might need to scrape off some of the old glue periodically, and re soak it.
When the splice is clean you can reglue it. Clean it up when it has set.
To prevent any chance of it coming apart, I would lay down a coat of epoxy all around the splice, then wrap it with a good quality natural string, like you would when serving a string. After it is wrapped, work epoxy into the outside of the string, so it soaks in.
As your bow works through the handle I wouldn't put dowels or pins to secure the splice.
Let me know if you want any more help.
Hamish