The two decided to part ways after a marriage of less than a year. Pacheco filed for divorce in December last year.
Pacheco is asking for primary physical custody but joint legal custody of their 22-month-old daughter, Ava Berlin, claiming that Renner's house is unsafe.
The documents cite the household hazards as an unfenced pool area and a gun and weapon collection, reported People citing court documents.
The actress and model has also demanded child support, stating that Renner, 44, earned USD 3.4 million in 2014 and has USD 13 million in assets. In addition, she's requesting USD 75,000 in attorney fees and USD 25,000 for additional legal expenses.