[Phanx]

All of these lines will break the default UI and spam you with "action blocked" errors:

MainMenuBar.ClearAllPoints = bottom 
MainMenuBar.SetPoint = bottom

OverrideActionBar.ClearAllPoints = bottom 
OverrideActionBar.SetPoint = bottom

PetBattleFrame.BottomFrame.ClearAllPoints = bottom 
PetBattleFrame.BottomFrame.SetPoint = bottom

You can't override methods on secure frames this way. Even your other idea:

hooksecurefunc('OverrideActionBar_SetDefaultAnchor', function(self)
	self:SetPoint(("BOTTOM", DataPanel, "TOP", 0, -3)
end)

... will throw errors because -- aside from having an extra parenthesis -- you can't move a secure frame in combat either. You are on the right track, however. You just need to add a combat check to your secure hook:

hooksecurefunc("OverrideActionBar_SetDefaultAnchor", function(self)
	if not InCombatLockdown() then
		self:SetPoint("BOTTOM", DataPanel, "TOP", 0, -3)
	end
end)

You may also want to add a "queue" so that any frames that were moved during combat (when you can't move them) can be moved after combat ends:

local queue = {}

local queueHandler = CreateFrame("Frame")
queueHandler:RegisterEvent("PLAYER_REGEN_ENABLED")
queueHandler:SetScript("OnEvent", function(self, event)
	for i = 1, #queue do
		local frame, pointA, anchor, pointB, x, y = unpack(queue[i])
		frame:SetPoint(pointA, anchor, pointB, x, y)
	end
end)

hooksecurefunc("OverrideActionBar_SetDefaultAnchor", function(self)
	if not InCombatLockdown() then
		self:SetPoint("BOTTOM", DataPanel, "TOP", 0, -3)
	else
		tinsert(queue, { self, "BOTTOM", DataPanel, "TOP", 0, -3 })
	end
end)

Your other option, as you said, would be to hide your data panel while in a vehicle:

DataPanel:RegisterUnitEvent("UNIT_ENTERING_VEHICLE", "player")
DataPanel:RegisterUnitEvent("UNIT_EXITED_VEHICLE", "player")

DataPanel:SetScript("OnEvent", function(self, event, ...)
	if event == "UNIT_ENTERING_VEHICLE" then
		self:Hide()
	elseif event == "UNIT_EXITED_VEHICLE" then
		self:Show()
	end
end)