An improvement is depreciated, not expensed. The cost of the addition is added to the cost basis of the house, which affects your capital gains calculation when you sell. Then, you can list the addition as an improvement in the home office worksheet. An improvement that is only used for the business can be 100% depreciated as a business expense, but that still means deducting the cost spread out over the depreciation period (which I think is 39 years for business property). There should be a way in the home office interview to add that you made a home improvement, and the program will ask what percentage of the improvement is allocated to the business. For example, a new roof improves the whole house, so only a percentage is allocated to the business, but a playroom addition that is only used for the business would be allocated 100% to the business.
You depreciate the entire cost of the addition when the addition is "placed in service" (when it is finished, inspected if necessary, and you start using it for the business) even if the actual cost is spread out over more than one year. The cost for depreciation includes the cost for materials, labor you pay other people, and the cost of necessary blueprints, permits or inspections, but you don't get to add anything for the value of your own (or your spouse's) labor, since you aren't paying anyone for it.
Also, of course, after the addition is put in service, it increases the overall percentage of the house used for business, so you will get a slightly increased deduction for mortgage, utilities and so on. Suppose the house is 2000 sq ft and the day care is 400 sq ft, or 20% of the house. If you add a 400 Sq Ft addition, now your day care is 800/2400, or 33% of the house, so you can deduct more of the other expenses.