To more effectively achieve teamwork in public games please be polite.
Command channel -
Ask your fellow squad leaders if they can do x. Do not tell them to do x. Alternatively make a suggestion that x will benefit the team. Providing information and sharing plans is the best use of the SL channel.
A squad leader has decided to take responsibility and usually has a plan. They are likely to have their own agenda and therefore ordering them to do something is just wasted words. The other squad leaders can swap teams or servers but beyond muting you they have no option but to work with or against you. When you ask for something to be done they are more likely to comply and will apply local intel to the problem so the solution is better as well.
The commander is just another squad leader. They should follow the same rules. They may have more information to share.
Don't be surprised when people say no to your order. You have no authority beyond your own squad and just sound like a d!ck to all the other SLs. Your method of communication is the problem here.
Squad channel -
Ask your squad members to do x. If this fails then you can tell them do do x, they have a choice to leave your squad but give them a chance to explain why they are not able to comply. I find that sharing my plan with the squad and asking for their help means I can concentrate on more immediate problems and know that a task will get done without further input from me.
"Can someone please recover that logi?"
"Bob you are nearest to the dead medic, please get him up."
Your squad members are different to the SL group, they usually need to be fed information and often reacting to changes quickly and decisively will swap the balance from loss to win. You as the SL have a responsibility to the team and should use your squad members to help the team. Remember your 9 man squad often makes up 20% of the whole team so most of them should be near an objective or helping to secure one. Asking your squad to move to the nearest flag or to hold or assault an area is the most common communication. Split squads also happens, just keep communicating the overall plan. Don't micro-manage just politely share what you want to happen.
Losing is inevitable sometimes but taking on a task that helps the team can be a mini win and keeps it fun for everyone. Be polite in coms and watch your success improve as a squad and as a team.