Syndicated Chat Routing

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 I am currently on August 2014 version and will soon upgrade to May 2016.  I am attempting to setup a syndicated chat widget. .  I have it working, but it keeps routing to the default chat queue and I want it to go to another queue.  Do I need to have the engagement engine to do such routing?  I played around with the chat rules, but they seem limited as I do not see a way to state if the chat initiates from this syndicated widget then assign to a specific chat queue.

Also, can I set different available chat hours for different chat queues. The agents responding to these syndicated chat requests have limited hours compared to our other chat agents..