If they spend the night then it counts as time lived with the other parent, not you.
More than half the year to the IRS means 184 nights or more (in a leap year - 183 nights in non-leap year) that do not need to be consecutive.
See Custodial parent and noncustodial parent in Pub 501
https://www.irs.gov/publications/p501#en_US_2018_publink1000220906
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**
