Military Family Stability Act of 2017 This bill allows a member of the Armed Forces undergoing a permanent change of station and the member's spouse to elect jointly that the spouse may relocate to the new location at the time during the covered relocation period as the member and spouse jointly select. A member and spouse may make such an election if: the spouse is employed, or enrolled in a degree-, certificate-, or license-granting program, at the beginning of the covered relocation period; the member and spouse have one or more children in school; the spouse or children are covered under the Exceptional Family Member Program; the member and spouse are caring for an immediate family member with a chronic or long-term illness; or the member is undergoing a permanent change of station as an individual augmentee or other deployment arrangement. Families with other needs may receive exceptions granted by military commanders on a case-by-case basis. A member undergoing a permanent change of station who has one or more specified dependents and is no longer married to the individual who is or was the parent of such dependents at the beginning of the covered period of relocation may make an election that such dependents relocate to the new location: by the member alone, if the former spouse is dead or has no custodial rights, or by the member and the former spouse jointly in all other circumstances. A member may not make: more than three elections; or any election unless the member's period of obligated service, or the time remaining under the member's enlistment contract, at the time of election is at least 24 months. The bill prescribes related housing and housing allowance requirements. Transportation allowances authorized for personal property of a member and spouse may be allocated as the member and spouse select. The Department of Defense shall establish a single application approval process for coverage under this bill, which shall apply uniformly among the Armed Forces.