It does sound good, but I was confused by your "need" for four ports. I would have though one would be enough, to feed the one you currently distribute from round the house.
If that doesn't have a spare ethernet port for the input a small switch should work fine, or maybe feed one of the Access Points from a later one.
Edit: Just realised, my idea probably requires gigabit ethernet between the wireless router and the current main one.
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Edited by RobertoS (Fri 12-Oct-18 14:52:11)