Yes they can,
This is one of the many inconveniences of military life for families.
This is not retaliation and totally on the level. Most units do the same thing. Those that do not want to participate are detailed with the setup and cleanup. I would suggest this Soldier speak with his 1SG about being detailed to the setup portion and not the cleanup portion. However, there is not an issue for the Soldier to be detailed to both. He has options, Soldier can try to submit for 1 day of leave, spouse could take a personal day or vacation day from her work if possible or hire a babysitter. If money is the true issue the Soldier should consider speaking with the PSG/PTLDR or Unit 1SG and/or Commander