UPDATE:

 

Running on DNN 4.5.5 I have been unsuccessful running cute chat on Child portls. However, when I chnage the alias of the portal to a parent <test>.<DomainName>@com the Cute chat authentication worked !!!!

 

I am still diggning into the URL re-writes to see if I can find where ut is breaking Cute chat.

 

I will post again when I find the problem area....