In ancient times, how would one protect his land from foreign armies while he was away on offensive campaigns?

They didn't.

That's how England was defeated. In 1066, the English king, and army was in the North, fighting off the Danes when William the Conqueror invaded in the south. The English rushed south, and arrived all tired. They lost.

His slaves would willingly protect his land and family while on campaign if he was a good slave master.

diplomacy ensuring noone is stabbing your back.

sometimes, it did work. other times, it didn't. there were times where people were stabbed in the back by their own family staying stateside (Richard Lionheart vs. John Lackland)

quite often, they took hostages on the campaign so that their bannermen and formal allies remained loyal.

no, his forts would be fortified and protected by the garrison and loyal people. If he was a bad leader his people would revolt while he was gone and hed have to fight them off when he came back.

usually there is a capital army and a capital guard, you know like the people with cannons on the walls or archers and tar bucketers who would stop them from climbing up or trebbing the gate.