When a remand is ordered the trial court is supposed to rehear the case based on the rules outlined by the Supreme Court. If the trial court does their job properly then the new ruling would stand. If they don't do their job properly then it would be up to the party who prevailed at the Supreme Court level to take the matter back to appeals.
I will give you an example of a real case. The Supreme Court ordered a custody case to be reheard on remand. Instead of rehearing the case the judge simply issued a new ruling with a bunch of made up reasons for the ruling, with the same result as the original case. So, the case went back into appeals and eventually got back to the Supreme Court and this time, instead of remanding the Supreme Court simply overturned...in other words, cancelled out the judge's ruling entirely.
The process of remand is honestly quite complicated and honestly depends a bit on the trial court judge's ego and how seriously the judge takes the remand...and to a great extent how far the judge believes that the parties will take the case. Getting remanded is a slap to a trial court judge...getting overturned entirely is a much bigger slap.
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I completely agree...hence the example I gave.

