IOTA client will redo the POW for 2 transactions. But what exactly is happening at the full node?
How will it keep track of all the reattachments?
What will happen if I reattach on multiple full nodes?
The re-attached transaction will be stored in local tangle of the full node and broadcasted to neighbors.
The full node won't keep track of the reattachment. The re-attached transaction is seen as a new one. (As it is a new transaction, there is more chance that it get picked by new transactions for validation.)
If you reattach to multiple nodes : every re-attached transaction will be seen a new transaction and broadcasted on the network.
Soon or later one of those will be confirmed, all the other will never be confirmed.