The bot is connected to an irc server and so are you right, so as far as the IRC sever sees it your clones as your on the same ip. (lets call it 123.123.123.123)
Even tho with in your LAN your on different IP's lets say 192.168.0.50 (bot) and .100 (you).
Now if the bot is giving off the 123.123.123.123 as its $ip which under most cases they do (/localinfo -u) then when it tells you to DCC CHAT to it it well tell u IP 123.123.123.123, which you likely cant connect to (some ISPs you can,most i have seen it doesnt work)
Now if the bot is giving off the 192.168.0.50 (/localinfo -h) as it $ip, then you "should" be able to conenct to it fine, but no one else outside your LAN well be able to as thats not the WAN (internet) Ip its at. I said "should" becuase as i beleive you may have said, even when its set to this IP it still seems to change, this is likely the NAT in the modem/router it intercepts the 192.168.0.50 and goes, "well sunshine thats your IP on the LAN, so ill just quitley change that to the WAN IP 123.123.123.123", thus your still seeing it as the WAN ip that you cant connect to.
(I said u trying to conenct to the bot, but the same thing applies if its the bot trying to conenct to you)
You might try looking under any advanced routing options, im not sure but i think its PVC routing settings or policies, you can define a IP or IP range and/or port range within the IP(s) that is outside of the LAN and should a attempt to contact/connect to that IP be made from within the LAN, that the IP your attempting to contact well be altered to some other IP you can set,
So you can say something like destination="123.123.123.123@ports5001-5010" replacewith="192.168.0.50@baseport5001", then any pc on your LAN trying to connect to 123.123.123.123 on ports 5001,5002,5003,5004,5005, well get there packets redirected to 192.168.0.50 on ports 5001,5002,5003,5004,5005"
(i might be wrong on it being the PVC settings but its in there somewhere (on this router at least), but i cant reach my Router settings from here to check sorry)
*** of course im not saying this is the only solution, or even the actual problem you have, I might be miles off target ***
