Can I manually control reinforcements during battles?

Yes, as long as they belong to your faction and are led by a General. To put reinforcements under manual control, follow the instructions below:

When you instigate a battle on the Campaign Map, the pre-battle screen appears, showing yours and the enemy's army. Tap the Reinforcements button above your army to view your reinforcements, where available. If a reinforcing army belongs to your faction and is led by a General, you can uncheck the AI control box (represented by a gear icon), and that army will be under your control when you start the battle.