Can a soldier who is married and receiving BAH be forced to reside in the barracks? Any regulations supporting it?

Yes AR600-20.

Yes they can. I am case in point. My (now) ex-wife and I were split. She moved back to her home state to start divorce proceedings. We were living in On Post Housing. I was ordered to vacate and clear housing and move into the barracks. BAH was initiated as I was to pay her the BAH until the divorce was final.

Many a time a leader has asked the CO to restrict a married person to the barracks for any violations- late/tardiness/missing formations/missing equipment, etc. The list can be massive, living in quarters is a privilege- not a right. Hell screw up with the housing people and thetr regs and you will be on the street!