Son acting out

My son is 6 years old. His father and I broke up about three years ago. Since then, I met a man and we got married and now have a one year old together. My oldest son rarely ever sees his dad. Lately he started acting out, telling me I’m stupid, that he hates me, talks back, is very mean to our youngest son and is very VERY ride to my husband/his step father. He tells me he only wants to see dad or grandma. Nothing I do is good enough or compares to them two. I do give time outs, take things away, but that really makes him more mad and just starts a whole new fighting match. I don’t know what else to do. He used to talk back, starting when his dad and I broke up and it’s gotten worse since then. I don’t know what else to do. Today his dad texted me (one weekend he surprisingly took him) and said our son told him that I locked him in his room, wouldn’t give him food or nothing. This NEVE happened. I didn’t even give him a time out in the last month or so it’s not that he mistaken that for a time out. I’m very hurt he is saying these things because I’m the one that is mostly caring for him and his dad barley does anything but he seems to be getting all the credit