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"The Pope can pick who is in union with him, and who is not."

Nonsense. He can't IMPOSE schism. It either exists in reality as a fact or it does not. He can't decide this unilaterally. Such a notion is absurd.

No he didn't impose Schism, he observed Schism. The erst wile Bishop, Mons. Fellay laid out these conditions:
Bishop Fellay: We are firm but not unreachable. Doubtless doctrine is fundamental, but we do think there are some preliminary stages to go through. That is the reason why, from the very beginning, we proposed two preliminary conditions to the Roman authorities. These conditions would make it possible to create an atmosphere of confidence which would be favorable to solving the problem of Ecône. These conditions are: the withdrawal of the decree of excommunication against the bishops of the Society and the acknowledgment of the right for every priest to celebrate the traditional Mass.

In them he acknowledged the excommunication, something you would not do. He made no mention of schism, but the Pope and Ratzinger used the term "schismatic mentality", this seems to be a limbo like state between union and schism.