Hello Amy,
I'm sorry to hear about your mum and about the upsetting dreams you have been having. I am no dream expert, but to me, it sounds like subconsciously, you are still upset that your mum suffered such a lot before she died and the second dream is just you thinking about that when you are asleep, but not reacting because you already know she is gone, so have got past the stage of a hysterical reaction.
The first dream sounds like you are just missing her. Much as your mum may have hoped raising you to be independent would mean you would not miss your parents after they were gone, that cannot really ever be the case. Of course she didn't want to think of you being upset that your mum and dad were gone, but the truth is we will always miss our mum and dad. They were the biggest presence in our lives whilst we were growing up and we are always going to miss them. I found this site after my mum died two years ago and I can not yet say I have recovered from that. My dad died in 1985 and I still miss him and think of him every day. I still talk to their pictures at home too! You come to accept that they are gone, but I don't think you ever stop missing them.
Your loss of your lovely mum is still very recent and even if you think you have started to feel better, it only takes something small to upset you again and that's how grief is. It is a roller coaster ride with ups and downs and upsets and then a few better days or weeks, then you get upset again. It takes a long time to recover from it, because it changes your world and changes you and that all takes a long time to adjust to. Just work at it one day at a time.
You say you still dwell on the days when your mum was still suffering and can see only that face and not the peaceful one she had after. That is normal for all of us. Your mind does tend to dwell on those horrible last days and weeks and months, but what you have to remember is that that period was only a short one in comparison to the majority of her life and it is her whole life that counts, not just the end of it. Try putting some pictures of her around from happier days. That helped me and revisit some of the places you spent happier times with her in. That helped me too. It was sad to be there without my mum, but it did help me remember the happy times we had spent there together.
As for the bad dreams, that sounds like you are still just upset and your mind plays on that when you are asleep. I've had a few bad dreams too, but that is all they are, just dreams. Pay them no heed. I suspect they are just you dwelling on your grief and worrying about your mum and where she is now and how she is doing when your mind is allowed to follow its own course, which is does when you are asleep. I think this will get better, Amy, but I think that will take time and a bit of effort on your part to redirect your thoughts and accept that she is gone and that there is nothing more you can do for her now and you just have to remember that she is no longer suffering and instead hope and believe that she is in a better place, reunited with those she loved and lost, as we all hope for our lost loved ones.
Sending you a big hug, Amy. Stop dwelling on the horrible dreams!