Almost certainly not, and the circumstances make it even less likely than a standard transfer request would be.
When a probation violation sentence is imposed, it is handed down by a specific judge in a specific jurisdiction, and that jurisdiction retains authority over the offender for the duration of the sentence. Louisiana sentenced them, Louisiana supervises the violation time, and Louisiana is where that time gets served. State systems are entirely separate from each other with different regulations, different facilities, and no obligation to accept or house another state's violators.
Interstate prison transfers do exist as a mechanism, but they are used sparingly and typically require compelling circumstances, such as a serious medical need that can only be met at a facility in another state, or a safety situation that cannot be managed within the originating system. A preference to be closer to family in Utah does not clear that bar, particularly for someone serving a probation violation sentence.
The probation violation piece makes this even harder. A judge who granted early release through probation and then watched that opportunity get squandered is not predisposed toward extending additional flexibility. Violators are generally not in a position to ask for favors from the court or the corrections system, and a transfer request in this situation is likely to be viewed as another example of not taking the situation seriously.
The realistic expectation is that the violation time gets served in Louisiana where it was imposed. The energy is better spent on ensuring good behavior inside and building the strongest possible record for release rather than pursuing a transfer that is unlikely to be approved.