He continued with the abusive texts, saying he would be over that night and would cut her head off.
He referred several times to the victim being dead, said he would have her bleeding on their son before police arrived, and that he would stitch their son into her stomach.
Defence lawyer Frank Minehan said Peachey had since been attending private counselling, which could include relationship counselling.
Judge Tony Walsh said he had concerns about what was going on in Peachey's head.
"When you make threats like that people don't know ... clearly the threats were made to upset [her].
"When he starts threatening to stitch the baby in her stomach, that's really sick and he needs to understand that.
"This is just unacceptable stuff and I think we need a thorough assessment done."
Judge Walsh said the threats were very serious and Peachey was playing "mind games" with the victim.
"There is something sick about what you said to her, especially the threats to harm your own child."
Judge Walsh ordered a temporary protection order against Peachey.
He was remanded to reappear on July 18 for sentencing.