Hey Agentv, Have you got this working already?
As I understand you have three orgs with a bot connected to each other by a 4th bot's privategroup right?
Sure the connection like this is possible but it would require to change quiet a lot of code in your bots (recoding the raffle.php module in all three bots to send the commands to the 4th bot) as far as the relay module is mainly made for the chat functions.
It could be possible to make this by setting the relaybot as a mainbot and the other three as a slaves + set the relay of the mainbot to the other three bots. Teoreticaly if someone in one of these three orgs would do a !raffle join in org channel it would be send to the mainbot and the relay function would let all the three orgs know that someone has joined a raffle.
NOTE: You would have to set the mainbot only as a bot for the raffles. All other commands would mess around in other three orgchannels.
I suggest you to make a raidbot for all your three orgs and just do a raffle in the privategroup.
Otherwise you can just set the !raffle join permission to ANNONYMOUS and anyone of your three orgs can just join the raffle on a bot which has started the raffle by "Click to Join" button if the relay already works for you.
Let me know how have you solved this if you have.