This topic wasn't highlighted in the Meeting Survivor's Needs survey of domestic violence shelter residents but it might exist under conflicts residents have related to a shelter's rules.
From the Quad City Times:
DES MOINES [Iowa] — Victims of domestic violence should be able to seek court protection for a family pet to keep an abuser from causing harm to an animal or using a pet to gain leverage, advocates said Wednesday. [...]
As a potential remedy, legislation is working through the Iowa House and Senate that would expand the scope of judicial restraint in domestic abuse cases to include specifically named pets. Domestic-violence victims could petition the court to require that an abuser stay away from the family’s animals, as well as the victim and the children, under the legislative proposals.
A judge could issue temporary and permanent orders granting exclusive care, possession or control of a family pet. The court action also could order an abuser to stay away from the animal and forbid the abuser from “taking, transferring, encumbering, concealing, molesting, attacking, striking, threatening, harming, or otherwise disposing” of the animal.
This update is needed and similar legislation should be introduced in other states. Legislators in Maryland are considering similar legislation and other measures related to domestic violence. Unlike many other types of legislation this is not an expensive change.
Without this change judges may decide to include animals if those seeking orders realize they can make this request, but their inclusion still needs to explicitly be part of the official system. This protects both animals and the people who care about those animals.
Along with this change needs to be more coordination between animal shelters and domestic violence shelters so that concern for animals doesn't prevent any adult or child from seeking safety.