Douglas hadn't fallen out with the southern branch of his party, but he wasn't the "doughface" that Buchanan was. Unlike Buchanan, he probably won't secretly encourage the Supreme Court to use the Dred Scott case to rule on slavery in general or influence northern members of the court to vote with the southern majority.
I see two likely options. The Court rules as it did, but it is more obviously an attempt by the south to dictate to the rest of the country. The clear spilt in the Democratic party probably leads to bigger divisions between the northern and southern parts of the party. OTOH, with the Democratic party less obviously in the hands of "Slave Power" there will be less northern Democrats switching to the Republican party.
If Lincoln does debate someone in 1858, it won't be Douglas. This could help Lincoln if the other speaker is not as good a Douglas, but the state legislature will still pick the Democrat along party lines.
OTOH, the Supreme Court could just uphold the Missouri state court without further comment. This possibly avoids the Panic of 1857, keeps the Kansas-Nebraska act intact and might even settle things enough to avoid the Civil War.
If the Democrats don't split in 1860, then Douglas probably get re-elected. If they do split, the Republican candidate, likely Seward, wins the election. The second will probably lead to a secession attempt, the first could still do so.
I'd expect Douglas, a strong Unionist, to make much more decisive actions than Buchanan trying to prevent secession.