I've just read 1 Kings 11-14, and there's no mention of Shishak attacking anywhere but Jerusalem. All it says is that there was continual war between Rehoboam and Jeroboam (14:30). If Shishak had attacked the north as well, surely Jeroboam would have been a bit busy defending against the Egyptians to be fighting Rehoboam? Yet Shoshenq invaded Judah and Israel. Does the wrong Shishak need to sit down?
How do you think he managed to get an army to Jerusalem?
The 'Bubastis gate' records several areas in which he tried to reimpose Egyptian authority.
Remember that the whole region had been virtual Egyptian property since around 1800 BC, and stelets had only recently made a grab for freedom when the Egyptian state threw an internal wobbly around 1000 BC.
In effect, Sheshonq was simply emphasising Egyptian control.
Archaeology from what is now Syria, Palestine and Israel gives ample evidence of his presence from seals, inscriptions, dtelae fragments, scarabs and a particularly fine statuette of the king as the Memphite war deity Ptah, found outside Jerusalem in 1976, now in Tel Aviv university museum.
The inscription reads
"...Hedjkheperrure Setepenre, victorious, given life in the mansion of Ptah before the miserable taken places, finding that which is his in eternity..."
Typical Egyptian bombast saying "Hey, I'm the boss, standing here, taking back what's mine already...."