You have not said how long ago you stopped living with your spouse. IF you live apart for at least the last six months of 2019 and the children are with you, then you can file as Head of Household. If it has been less than 6 months then your filing choices will be to file married filing jointly or married filing separately.
If you do not qualify to file HOH, then hope you are getting some legal advice ASAP, because you will need it. We cannot give legal advice here.
Here are the "rules" that you have to follow if you file MFS:
JOINT vs. SEPARATE RETURNS 2018 and beyond
If you were legally married at the end of 2019 your filing choices are married filing jointly or married filing separately.
Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $24,400 (+$1300 for each spouse 65 or older) You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit.
If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states: AZ, CA, ID, LA, NV, NM, TX, WA, WI) If you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.
https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately
https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states
https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separ...
IF you do file HOH and your spouse files first and claims the children, you will have to print, sign and mail your return claiming the children. Then the IRS sorts out who should have claimed them.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
