also referred to within the EU as a “barring order”

“there are the orders that provide immediate protection. The emergency removal order (also called ‘go order’ or ‘barring order’) is relatively recent, but is being widely adopted. Following Austria,which introduced it in 1998, it can now be imposed in 11 Member States (AT, CZ, DE, DK, FI, HU, IE, LU, NL, SI, SK). Such an order allows the police (sometimes operating under the authority of either prosecutorial or an administrative authority) to temporarily ban the offender from the home (the range of the ban varies from 3 to 20 days, with a possibility in several Member States for an extension underspecified conditions). In some Member States the removal order is embedded in a multiagency intervention programme for both perpetrator and victim/s (AT, NL). Some laws allow the police to impose a ban regardless of the wishes of the victim, if the perpetrator poses a danger.” (p. 63)
“by giving the police power to remove the person posing a danger from the home (emergency removal orders)” (p. 202)
http://www.europarl.europa.eu/eplive/expert/multimedia/20110...

in Australia and New Zealand, referred to as a “police order

"The key enforcement initiative is the introduction of an 'on the spot' order issued by the Police for the purpose of protecting victims of domestic violence. These Police orders are most likely to be made when the Police have been called to a domestic violence incident in the home. The purpose of the Police order is to ensure the immediate safety of the victims by removing the alleged violent person from the home for a period of up to five days. The order will provide a period of safety in which victims can consider their future options. The victims' consent to the order will not be required."
http://www.parliament.nz/en-nz/pb/legislation/bills/digests/...

If you want to translate “institut” more literally, consider “concept” (i.e. “the concept of an emergency removal order”), but I don’t think it’s necessary


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Note added at 9 hrs (2013-08-27 05:06:31 GMT)
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Part Two of your question (“zákaz přiblížení”):

“zákaz přiblížení” is part of the “removal order”, i.e. it is not technically a “restraining order” as this needs to be imposed by a court (I stand to be corrected). I would use something in the vein of “prohibition of approaching the victim” (might need polishing though). The example below is not ideal (it concerns criminal proceedings), but at least indicates a precedent for my suggestion:

“… u trestných činů spáchaných v rodinném kruhu ukládá uložit původci násilí zákaz přiblížení se k oběti…”
“… where crimes are committed within the family, prescribe that a mandatory injunction is to be imposed on the perpetrator of the violence prohibiting him from approaching the victim…”
http://europa.eu/rapid/press-release_CJE-11-48_en.htm