boyfriend wont stop talking to his ex! says he misses her.

When i met my now boyfriend he was living with his ex. She has a new biyfriend and he now has me. Long story short they broke up because she cheated on him with her now bf. Well, recently she called the police and accused him of chocking her (which was a lie. She amitted that on video) since then she moved out and was able to get her name off the lease. I moved in shortly after. They were together for 7 years and he says that hes two dogs are like their kids and he doesnt want to keep her from seeing them. I personally thing he should stop talking to her after everything she has done but he keeps giving her excuses for her actions. How should i handle this? Should i just leave him. I saw their text and he said he missed her. Im so hurt idk how to feel.