How to solve replication in MongoDB only with two machines?
We know that the Replica Set does not work by itself with two machines, but we have this limitation.


If your goal is high availability with automated failover I would definitely aim for a solution that does not involve reconfiguring the replica set or allow for the possibility of multiple active primaries. 

Ideally this does require a third machine so you have a tie-breaking vote to allow  either MongoDB 1 or MongoDB 2 to become primary in the event of a partition between the two. The third machine can either host another secondary (recommended) or a voting-only arbiter (not recommended for HA as it cannot contribute to majority write acknowledgement).


  Whenever Wildfly 1 drops, Wildfly 2 raises by reconfiguring MongoDB 2 to be primary by changing the settings of the ReplicaSet.


If MongoDB 2 is a secondary, this scenario only works if you force reconfigure (since a majority of voting replica set members are not available).

As noted in the documentation, force reconfiguration is a last resort for recovering a replica set rather than a procedure you should frequently use or automate:

Use this procedure only to recover from catastrophic interruptions. Do not use force 
every time you reconfigure. Also, do not use the force option in any automatic scripts
and do not use force when there is still a primary.



  If a split occurs on the network, Wildfly 1 continues to work writing in MongoDB 1, Wildfly 2 is also active, changes the MongoDB 2 configuration to primary, and begins writing to it.


A primary can only be elected or sustained in a partition with a majority of voting members. With only two voting members, a network split will result in the current primary stepping down (since it can't see a majority of the voting members) and no primary elected.


  What happens to MongoDB when reestablishing the network and Wildfly 1 take over as principal?


If you forced MongoDB 2 to become primary, it will have a replica set configuration with a significantly higher replica set configuration version. MongoDB 2 may also have writes that haven't replicated to MongoDB 1 yet, so there are two stages of recovery:


If MongoDB 1 accepted any writes that were not replicated to MongoDB 2, MongoDB 1 will enter rollback mode to try to revert write operations to a common point in the oplog. If too many operations have been written on MongoDB 2 or MongoDB 1 no longer has a common point in its oplog, MongoDB 1 will have to be resynced.
Assuming both members now have a consistent oplog history, MongoDB 1 will resume syncing (as a secondary) to try to catch up write operations that have been applied on MongoDB 2


If both of those stages are successful, MongoDB 1 should be eligible to become primary. MongoDB 1 won't automatically become primary unless it has a higher priority than MongoDB 2.