Are we legally able to get our deposit back if my wedding venue didn't disclose that they would be open for business during my private ceremony?

You are concerned about the deposit, when what you should be concerned about is having to pay for an entire wedding party that you committed to hold at the venue by making your deposit. When you make a deposit with a wedding venue, they hold the time and space open for you and turn away other weddings and parties. Talk to a lawyer in your area. Most venues remain open for public business during a wedding. Many venues have multiple parties going at once. The issue is whether there would be actual foot traffic or noise carryover into the room or space you are using. Almost any restaurant, hotel, or banquet place will have other parties and customers, though not in your exact room or space. The thing you are considering a breach of the agreement may not be that at all. It may be the way most party venues run their businesses. You also may be imagining that it will be different elsewhere, and it may not be. If you want to rent out a place to have the entire location 100% private during your wedding, this will cost a lot, unless it is a tiny place that truly can only accommodate your party, such as a historic building that is rented out for parties. Even then, you must always ask. As an example, I lived for a while in community of people in the arts that was in a beautiful old historic building. The first floor was rented out for weddings on some weekends. There were quite a few brides horrified on their wedding day when they saw all the ragamuffin sculptors, filmmakers, musicians, dancers, and poets coming and going through the front hallway. Always ask who may be in the venue during your wedding.

It may depend upon a number of things, including how close to the date this is happening. Ultimately, the terms of any contract you signed will determine if you get some or all of your deposit back.