Hi Molly,
I am so sorry for your loss and understand how hard it must be now, losing your lovely dad and looking after your mum. I lost my wonderful dad in 2010 and was carer for my mum for a long, long time, the last 7 years of which was filled with dementia. She died in October last year and I miss her to pieces - it's incredibly hard.
I too felt very alone when Dad died, but I knew I had to focus on mum's needs - that was the only thing that got me through the misery of grief at the time. Dementia is a very scary, isolating disease, and many times I felt scared and isolated, but now mum has gone, I miss the caring so much and miss her beyond belief - and the memories of dad have come back renewed.
Some carers miss caring; others are relieved the caring is over. I am the former. No-one should ever say that you shouldn't feel such a loss because it was a parent you lost - as if losing a parent is expected. I have had that said to me and it infuriates me so much. Loss is loss - it's the loss of the that person and what they mean to you that is important, regardless of who they were.
You grieve any way you want to but please try and get support - counselling if you can - and I hope you have help with your mum. Carers are so important at this time, and they can also be company for you, to break up the day (I was assuming mum is living with you but i may be wrong)
If it helps you, keep posting here with your struggles, your thoughts etc. Everyone here will support you. We can see how much you adored your father, how much you struggled and how much you continue to struggle. I struggle every day so I know that feeling. All i will say is the struggles and pain you feel are testaments to your love - that's the only good thing I can say about grief......