How should I deal with unruly soldiers who are belligerent and demonstrate no drive to improve?

Counseling statements. Start with (if you havent done so) the initial counseling outlining your expectations of them and what they can expect from you. In that statement, include what ramifications they can face if expectations are not met. Expectations to include duty performance, professional conduct, uniform, etc.. After that, counsel them every time they DO NOT meet those expectations and any acts of belligerence. Also, be sure to counsel them on any acts where they exceed those expectations. Gotta mix good with bad. Also, be sure that your NCOs have your back. If you need further guidance and assistance, hit me up in Enterprise. [login to see]

Also....and here is where the NCOs need to have your back.....after a certain amount of time and/or a certain number of counseling statements where they didn't meet standard...then submit a recommendation thru your Chain for Article 15 proceedings.

Document Document Document!!!!!

Congratulations on earning a position of trust and leadership. I’m sure you showed the ability and potential to perform at a position of a higher grade/responsibility.
I hope you have discussed the issue with your mentors already...mentors are not necessarily the leaders or NCOs directly over you.
Have you been laterally promoted to CPL?
Did your PSG and or 1SG empower you / give you authority to counsel the other SPC?
You need to be empowered by them to enforce your decisions to assign duties and divide the tasks that have to get done.
Don’t take it personal. It’s not. Professional v unprofessional conduct. Maturity v immaturity. But be in charge...that doesn’t mean dictate everything. Leaders have to perform as well. The “by example.”
Assign tasks based on talent & capability...and do it as a group huddle meeting. (Talent management at your level.)
Reward the PFC who performs, and starve the SPC’s bad behavior of attention. That doesn’t mean don’t address it, but when you do address it don’t be emotional. Be clear, concise, and reasonable.
Give 1 verbal, then put it in paper.
Also check your expectations. Perhaps the SPC doesn’t know how to do what you think he should know, or has never been held to accountability. And he/she has used the belligerence to deter other NCOs from Dealing w him. Perhaps he’s been there longer or you got better attention from your leadership and he/she is jealous of it.
So make getting the task done a competition (if you can) between him and a junior SM...or you and him. Can you create 2 teams and see which gets done fast and better? Ask the PSG or a SSG from out side your platoon to judge?
Or is there someone in your section w personal power...the guy that’s not in a leadership position but influences how the entire team operates and responds. Get the influences and motivators on your team (and not by outing the other guy, but by convincing him of your well meaning intention and potential and the necessity of the task). If the influencer is this SPC, then you need to steal the personal power by giving it to the next influencer. Understanding those under you, their talents and abilities, and who can influence who (positive and negative) helps you as the one in charge manage the talent and how to assign tasks.