Doing an OnEnter on the frame on top causes an OnLeave for the frame underneath it which would cause the closure of your information frame.
I don't know LibQTip or what else you might be using but you would need to implement a mouse check for the OnLeave to check if the mouse is still over the frame or not before closing
eg.
Code:
frame:SetScript("OnLeave" function(self)
if not self:IsMouseOver() then
-- do whatever to hide
end
end)
I don't know the best way to do it for you but it seems you have some time to play
Take care and be safe.