Mary, I'm so sorry to hear you're struggling. I can completely relate and all I can say is it will get better, but it takes time, lots of time. I lost my mom very suddenly as you did your dad. She went very fast, faster than any PALS I have read about.
I also completely relate to your puppy situation. I was nearly 3 months pregnant when my mom died. When I went into labor which should have been a very exciting and happy moment, all I could do is sob that I couldn't call my mom and tell her it was time. I cried all the way to the hospital with thoughts that she should would never see the baby and that was a full 6 months after she died. My son is almost two and I still look at him when he's doing something amazing and feel my eyes well up that she isn't here to see it.
I cried regularly the first year maybe year and a half. In fact I'm surprised I didn't lose my job because I became borderline dysfunctional. All I could do is cry and miss her. So everything you're going through is normal. One of my favorite quotes is "the only way out is through". You will just need to go through this and give yourself the time to grieve and feel the loss.
Other life problems led me to visit a counselor about a year and half after my mom died. I found once I got there what I wanted to talk most about was my mom more so than the latest life catastrophe. Maybe you would benefit from visiting a counselor if you haven't already. I know it really helped me processes a lot of things left unprocessed.
The good news is it has been 2.5 years and I am much more at peace with it. It still hurts, I still dream about her almost nightly, I still think of her daily, and I still just wish more than ever she was still here. BUT I rarely cry in fact I can't remember the last time I did and life is easier, the distress is gone and I am functional again, well most days but the days I'm not I now blame having a 2 and 4 year old
Hugs!