Speech therapy not going well

My 2 year old will be 3 this December and has yet to say any real words. Just simple "no, okay, and count to 3". His doctor recommended he'd see a speech therapist. He sees his therapist twice a week but it's not going well. He's very hyper active and doesn't want to learn anything. He sees it as play time and starts screaming if he's told no or if a puzzle is taken away. He spends most of the time throwing a tantrum and I can tell his speech therapist is getting annoyed. She raised her voice at him today and I'm thinking of cancelling his further sessions. Not because she raised her voice, because I get it. It's time being wasted she can be teaching but because I just don't think he's ready to be taught. Maybe he's still too young. And before anyone attacks me for bad parenting. I discipline often. I don't give him his way and I believe in not only discipline but time out. For his bad behavior I blame my mother and sister. We lived with them his first two years and they spoiled him incredibly and now I'm dealing with the aftermath. I feel I'm being judged, like I'm not a good mom and I am. I just don't know what else to do to get him to listen and learn.