Which of the four border states in 1861 (Delaware, Kentucky, Maryland, Missouri) was the easiest for the Union to maintain and which was the hardest?
I like the above response and think a good case is made for Missouri. I would argue that Maryland was more difficult to maintain in the Union. While Missouri was distant, a frontier state essentially, and the American/Union military presence there was minimal, there was not the population of Maryland in either whites or slaves, nor the danger to the Union if Maryland had seceded.
If Missouri had joined the Confederacy and the Union had not stopped them, the worst that would have happened would have been a delay in eventual Union victory. They still would have advanced from Illinois and/or Kentucky and occupied the Mississippi River, thus isolating Missouri regardless. If Maryland had seceded, the capital of the country would have been surrounded geographically by the Confederacy, and under siege. At the least, it would have had to be moved to New York or Boston, and this may have prompted British aid to the South.
Furthermore, Maryland had a very pro-secessionist population that gave volunteers, aid, comfort and supplies to Lee's armies as they marched North. Keeping them in line was definitely harder.
I think it is difficult to say which border state was the easiest to maintain. Lincoln worried about them all joining the Confederacy and each presented its own problems in maintaining them in the Union. But, Missouri was probably the border state that was most difficult to maintain. Missouri was considered a Confederate state by the Confederacy and a Union state by the Union. The Union had a star on its flag to represent Missouri and the Confederacy had a star on its battle flag to represent Missouri. Missouri sent troops to the Union army and it sent troops to the Confederate army. There was a brother against brother reality in the fighting in Missouri. There were more skirmishes in Missouri than in any other state except Virginia and Tennessee. Missouri had both a Confederate government and a Union government. Because of all these factors, Missouri was difficult to maintain in the Union.