Nothing is "written off." The sale of the home has nothing to do with your itemized deductions on schedule A or using the standard deduction.
Start by reviewing publication 523.
https://www.irs.gov/pub/irs-pdf/p523.pdf
1. Your gain is the difference between your selling price and your adjusted cost basis. Your cost basis is what you originally paid, plus and minus adjustments. Adjustments to the cost basis are listed in publication 523, they include permanent improvements (but not repairs), as well as certain of your closing costs from the purchase. You may have to reduce the home's cost basis if you used it for business or as a rental. You can also subtract the real estate commission from the selling price and possibly some of your closing costs, as listed in publication 523.
2. Your gain or loss is reported on a schedule D (if you need to report the gain). Any gain is taxed there. It doesn't have anything to do with itemizing your personal deduction (mortgage, property tax, etc.)
3. Property tax you paid, and mortgage interest you pay, is certainly deductible on schedule A, but if you are married filing jointly, your deductible expenses may be less than the standard deduction.
4. If you owned the home and lived in it as your main home for less than 2 years, you may still be able to use a partial capital gains exclusion if you are selling for one of certain listed "unforeseen circumstances". See page 6 of publication 523. Giving birth to a single child is not one of the listed circumstances that is automatically accepted by the IRS, but there is a general category for "other facts and circumstances." If you believe you can show that the birth of your child caused a significant financial hardship (considering your particular unique facts and circumstances) then you can claim a partial exclusion. The exclusion is time-based, and is based on whichever is shorter--the length of time you owned the home, the time you lived in the home, and the time since you last sold a home. For example, if you will have owned the home 600 days before you sell it, but you lived in it only 580 days, then your exclusion would be 580/730 x $500,000 = $397,000. (This assumes you are married filing jointly and two years equals 730 days.)
If you claim the partial exclusion, you don't send proof to the IRS with your tax return, but keep your proof for 6 years in case of audit.
