The honest answer is that your ability to influence a transfer from the outside is very limited, and going in with realistic expectations saves a lot of frustration.
Transfers in the federal system are driven by the Bureau of Prisons based on bed availability, security classification, programming needs, and institutional management decisions. Requests from family members carry very little weight in that process. The BOP is not structured to respond to outside pressure on placement decisions, and in most cases a letter or call from a family member asking for a transfer will be acknowledged at best and ignored at worst.
In federal prison, an inmate cannot even be considered for a transfer until they have served at least nine months at their current facility. The system wants a track record before it considers moving anyone. That track record needs to show excellent behavior, active participation in programming, and the kind of conduct that earns a step down in custody level. Transfers to lower security facilities, including those with work release programs, follow that custody level reduction rather than preceding it.
Work release is at the end of that progression, not an early option. An inmate works their way down through security levels by accumulating a clean record and completing recommended programming over time. A camp or facility with a work release component is typically the last stop before full release, and getting there requires the institutional record to support it.
The most effective thing you can do from the outside is encourage your person to focus entirely on their conduct and programming participation. That is what actually moves the needle on transfers and custody reductions. Nothing you do from outside the walls matters as much as what they do inside them.