Mark Hobson, 26, Brampton Meadows, Richard Savage, 40, of Masborough Street, both of Rotherham, were charged with stealing the dogs and a Dewalt angle-grinder, and possession of the imitation firearm, when they appeared at Mansfield Magistrates Court, on Friday.
The incident is alleged to have taken place on October 27.
Prosecutor Neil Hollett argued they should be remanded to custody because there were substantial grounds to believe they would commit further offences, interfere with witnesses, and fail to surrender to court.
Magistrates remanded them into custody until November 29, when they will appear at Nottingham Crown Court, via videolink.
For more cases from Mansfield Magistrates Court, click here.