And going off of that, what are some more notable examples of this?
Hmm...that's an interesting question, friend. While I wasn't able to find controversy over the creation of a monument to an individual Union or Southern Unionist figure in a part of the former Confederacy, I did find this news article on a related issue you would likely find interesting:
http://www.nytimes.com/2014/01/17/us/blue-and-gray-still-in-conflict-at-a-battle-site.html?_r=0
Essentially, there was a monument to Confederate soldiers at a battleground in Florida. Some folks wanted to erect a monument to the Union dead as well (the Union lost that battle) but were vociferously opposed; organizations such as the Daughters of the Confederacy claimed they merely did not want to change an established historical site. My skepticism of such a claim is obvious (I've precious little sympathy for the Confederacy or its defenders), but I'll say no more than that, both to keep on-topic and to maintain civility, as the rules recommend we do. So I'll just note that this does seem to be an example of a Union monument being opposed on Confederate soil, but it's the only one I could find.
Now, I would wager that a monument to, say, William T. Sherman somewhere in the South would garner a lot of opposition, because his "March to the Sea" and the destruction it wrought are still controversial even today. However, I haven't been able to find much controversy over Union memorials of any type in Southern territory. See this JSTOR article:
Frank Wilson Kiel, "Treue der Union: Myths, Misrepresentations, and Misinterpretations" in The Southwestern Historical Quarterly, Vol. 115, No. 3 (January, 2012), pp. 282-292, http://www.jstor.org/stable/pdf/41617001
In fact, however, at least ten places in ex-Confederate states, four of them in Texas, have monuments to the Union.12 Greeneville in Greene County, Tennessee, has a courthouse monument to the Union, erected by Burnside Post No. 8 of the Grand Army of the Republic.13 Cleveland, Tennessee (near Chattanooga), at the entrance to the town's Fort Hill Cemetery, has a monument erected by the Grand Army of the Republic "to perpetuate the memory of the boys in blue in the war of 1861-65 who have lived in Bradley County." Denison, Texas, has a monument to the Union in Fairview Cemetery at the place of burial of six Union veterans who settled in Grayson County after the war, erected by Grand Army of the Republic of Denison.14 In New Braunfels, Texas, in a downtown park, there is a "Monument to the Memory of our Fallen Soldiers of the Civil War 1861-1865," which honors soldiers of both sides of the conflict.15 Greenwood Cemetery in Dallas has a memorial erected by the Grand Army of the Republic in association with the graves of Union soldiers.16
I haven't heard of any controversy swirling up over those places. I suppose--perhaps--reasons for a comparative lack of opposition to Union monuments on Rebel soil might be found in books such as David Blight's Race and Reunion and Nina Silber's Romance of Reunion, which each explore (to summarize very succinctly two very extensive works) how the Civil War was recast as a noble struggle in which both sides, blue and grey, displayed manly valor (making them both "good guys," so to speak) and that neither had anything to be ashamed of. As Blight makes clear, of course, this approach might have helped the two sections reconcile, but it also papered over the role of slavery in causing the war and contributed to the persistence of racism in the succeeding decades.
Amazon.com links for the two books:
http://www.amazon.com/Race-Reunion-Civil-American-Memory/dp/0674008197/ref=asap_bc?ie=UTF8
Hope this helps at least a little bit!
what are some more notable examples of this?
Just a reminder to potential respondents: do not take this follow-up question as an invitation to simply post placenames, links, one-liner, or any other brief answer. Any answers in this subreddit should be in-depth and properly sourced. Thanks!