The 5-year-old boy and the 4-year-old girl allegedly had rope burns on their arms from being tied to objects in the home, were under-nourished and were injured from physical abuse, Lt. Ken Weaver said.
The alleged abuse had been going on since the end of May, Weaver said.
Edward Allen Kemp II, 24, was arrested July 22 on suspicion of assault with a deadly weapon and was released after posting $30,000 bail, Weaver said.
Kemp's mother, 45-year-old Klella Jo Farris, was arrested Aug. 3 on suspicion of assault with a deadly weapon and corporal injury to a child causing injury, Weaver said.
The children's mother and Farris were in a romantic relationship for more than a year, and she, Farris and Kemp all lived with the children in the residence in the 2700 block of Tuolumne Street, Weaver said.
Police began investigating the child cruelty allegations on June 28 after receiving information from Solano County Child Protective Services which took custody of both children, Weaver said.
The Solano County District Attorney's Office also investigated the case, police said.