If the property is owned equally then each owner will report their share of the proceeds on their tax return (33 .33% each). The mortgage can be a factor in ownership, if any estate or gift taxes issues arise. For example, mortgagee/owner of the property gifted 66.66% to relatives. Capital improvements increase the cost basis of the property when calculating gain.
When you sell a vacation home that you haven’t ever rented out, the taxation will be similar to that of a second home. The taxes will be calculated based on the sale price, less what you paid for the property (your cost basis). Just like a second home, the tax rate will be based on whether the property was held for more or less than a year. The IRS considers a vacation home a “personal capital asset.”
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