Chapter 3. I pretty much spammed Juggernauts/Iron clads and walked into the open territory with just 1 or 2 ground units. On Hard.
I think I see your problem.
Try spending some of that 1000 gold on ground units and sending those in with your other troops. You can't actually capture any territory at all without ground units. Invade a hundred, a thousand times with only air and sea, but all you'll do is kill the units there, you'll never take ownership. Boots on the ground is required.
I recently beat Chapter 3 on Hard. Did it in under 15 turns, too. I had a huge ground force, but after a couple of invasions that didn't go very well - even though the Undead liked me a lot. I instead held off for two turns to buy and send up reinforcements and that let me take the territory and win.