How can I drive my competitors bankrupt?

Late-game rival malls tend to start out with instantly capturing 80% of your regulars in all three areas. This sucks, but the counter is fairly simple:

Hold regular sales.

Aside from being a great income booster, in the later stages of the game (where you seem to be right now) you generally gain enough hearts from the sale to cover the cost, and sales = more visitors to that store = faster level gain = higher quality.

Also, if you haven't yet, spend some hearts on improving various stores.

And most importantly: During sales season, holding sales boosts your rep with each sale you're holding. Use that to ensure you have a frenzy going on -- massive popularity booster.

It may take a couple years, but if you keep an eye on the other store you'll notice when it starts losing customers to you.