R u using the latest version? In the most recent version of Wiigator's cMIOS there is an option for this when you boot from a multigame disc. So, if you burn both disc images to a multi-game DVD-R when you load it through GC backup launcher it will ask for which game you want to play. At this point you push Z (I think? The loader tells you which button) and you can select the second disc. I haven't used this method in a long time, but if I'm not mistaken when it asks for the second disc it'll automatically boot? I used this to play RE and Metal Gear Solid and it always worked better for me than actually swapping the backups.
I guess your 1st disc is on a multi game disc and the 2nd is a seperate disc? If yes:
It won't work in WiiGator's loader, in NeoGamma it should work as expected. If not select the GCM whatever thingy as 2nd disc and try it again. That might actually work in WiiGator's loader too.
If both discs are on seperate multi game discs:
Insert the 2nd disc in NeoGamma, press Z on the 2nd disc. Eject the disc, insert disc with 1st disc, and then play it. At the end of disc 1, switch the discs as expected.
If both discs are on the same multi game disc:
Just boot the game, at the end of disc 1, eject and reinsert the disc.
If both discs are seperate 1:1 discs:
It should work as expected in NeoGamma. If it doesn't that's either a bug in NeoGamma(and WiiGator's loader!) or there's something wrong with your burn.