3 year old behavior issues or normal?

I truly need some advice here. My son just turned 3 at the beginning of the month. Little backstory: I didn’t have a great upbringing. Alcoholic parents. And now my sons dad is an active alcoholic and opioid addict. There is absolutely no stability with him. When I was with him he was very abusive mentally and emotionally. My son endured so much yelling and I feel so much guilt and sadness for not realizing my sooner. Fast forward to right now: my son has been having tantrums. My mom was visiting from out of town and my son didn’t have a nap and apparently snapped on her and started yelling at her. I know that behavior is unacceptable. Now today he had another tantrum because he wanted me to lay down with him and as soon as I said his dads name he freaked out worse and bit me. I was talking to my mom after and she told me my sons not normal. He has issues. Then blamed me for his actions. Then she said I wanted him to hurt her and she was scared. I’m sorry for the rant but I use a gentle approach to parenting(at least I try my best) and am doing my best without ANY help. So is this normal for a 3 year old?!