It's difficult for me to discern exactly what you're asking, but let's just describe everything that happens when a leader rejoins after a partition.
In your scenario, when the partition heals and node 1 - the leader for term 1 - rejoins the other leader for term 2, the leader for term 1 can step down either as a result of an AppendEntries request from the other leader or response to an AppendEntries RPC from the other leader or a node that knows about the new term. Once node 1 steps down and increments its term to 2, nothing else needs to happen. The old leader - node 1 - will be receiving heartbeats from the new leader and so will never start an election, so I'm not sure why there's discussion of a new election. Only in the event that node 1 stops receiving heartbeats from node 2 (the new leader) will it timeout and start a new election. In that case, node 1 will indeed increment its term again to 3 for the new election. The fact that a node was previously a leader has no bearing on any future elections. The term is all that matters.
In practice, node 1 can actually step down before the partition heals. If a leader is partitioned from a majority of the cluster, it should detect that (if a leader can't contact a majority of the cluster for more than an election timeout you can assume a new leader will be elected) and step down so clients disconnect and try to find a new leader.