Civilization 5 – Why Is City Not Generating More Happiness After Purchasing Happiness Structures

In war the AI sometimes gives up and hands over like 12 cities at once for peace (which I'd be stupid not to take)

I think your conclusion here may be false. If those cities are going to drive your happiness into the ground, it may not be in your best interests to take all of them at once. There is no magical wellspring of happiness that will allow you to absorb an unlimited number of enemy cities into your empire without repercussions.

Use the following methods to increase happiness:

• Build courthouses in captured cities. This negates unhappiness from occupation.
• Get as many luxury resources as possible (by building the appropriate improvements on their tiles or through city-state allies). Look for resources just outside your borders and consider purchasing those tiles. Plan new city locations with an eye toward where you can get the most luxury resources.
• Build happiness-producing structures: Circus, Colosseum, Theatre, Stadium, and Burial Tomb if you're Egyptian.
• Build happiness-producing wonders like Hanging Gardens and Eiffel Tower.
• Get social policies (there are many) that work with your existing empire to increase happiness. Look at how they generate happiness, and find the ones that match your style of rule. Don't try to change your whole empire just to eke a little more happiness out of a social policy.

In addition, use puppet cities to your advantage, and don't overextend yourself. If taking all those cities is going to cripple you, it may not be worth it. Is a vast, dysfunctional empire better off than a slightly smaller, functional one?

I had a problem with this - make sure you're clicking on the hex tile at the unit's "base", and NOT on the circular icon for the unit. Clicking on the icon "selects" the unit and cancels the gift operation.