You really need to check with the council.
While not particularly a ‘relocatable home’ as it sounds like an existing residence, not a new prefab one, this is the only information on the BASIX website:
What is defined as a ‘relocatable home’ / ‘transportable home’ / ‘manufactured home’?
Certain types of dwellings such as relocatable homes, transportable homes and manufactured homes may be dealt with under the Local Government Regulation 2005. Dwellings approved under that Regulation rather than the Environmental Planning and Assessment Act 1979 are not subject to BASIX. It is a matter for the consent authority (Council or Principal Certifier) to determine under which regulation approval is required.
More information on transportable and relocatable homes and the application of BASIX can be found in Planning Circular PS06-18 http://www.planning.nsw.gov.au/planningsystem/pdf/circulars/ps06_018_transportablehomes.pdf
Does a ‘relocatable home’ require a BASIX certificate?
As a relocatable home is not within the definition of building under the EP&A Act (www.legislation.nsw.gov.au), a BASIX certificate is not required for this type of home.
For further clarification on the different approval requirements for a ‘relocatable home’, please refer to Planning Circular PS06-18 http://www.planning.nsw.gov.au/planningsystem/pdf/circulars/ps06_018_transportablehomes.pdf
In some cases, a Local Environment Plan or specific policy of Council requires approval for use of land under the EP&A Act and in these instances, a BASIX certificate maybe be required. It is a matter that the consent authority (Council) needs to determine on a case by case basis, dependent on the interpretation of the definitions in their LEP and policy documents.
As a relocatable home is not within the definition of building under the EP&A Act, a BASIX certificate is not required for that type of home. This is the case even if the installation of the home requires development consent. Similarly a relocatable home does not require a BASIX certificate when moved from one site to another site (because it remains a relocatable home).
However, in a situation where the original dwelling was not erected as a relocatable home, and thus are of the view that as it was never a relocatable home, its movement from one site to another is not covered by the above exemption to BASIX.
That logic appears sound however, Council would need to seek its own legal advice on the matter, as the BASIX help desk is not able to provide advice beyond what is in the Planning Circular.