The splitter IS NOT effecting the wireless
You MAY have a problem with the cable ends jumper from (splitter changes downstream by 8dB but upstream only 4dB?, make sure they are tightly screwed in) still CAN'T effect wireless
Router/firewall is showing unexpected states/sequences Could be an attack or just a verbose/over picky router (what brand and model? )
mrschultz02
is likely right, someone is stepping on your wireless channel and MAYBE (accidentally or not) crossconnecting at times (what are your security settings on the router? WPA2? (I hope)
None of this is a modem or splitter problem,
look carefully at the router WLAN setup