My mother too died in her late 60s but long before my father. He did keep up an extensive social life and also met and dated a few women. He settled on a very nice lady, lets call her Jean, and we were all glad she was in his life because he had companionship, laughter, did much travelling, and greatly enjoyed his life till 20 years later she too was struck down with cancer. It also meant we had less worry as to what he was doing, because there were two of them to tackle life's challenges, the bin men not collecting or the guttering falling off, or remembering/getting to hospital appointments etc.
He explained it to me like this: just because he was dating another lady didn't in any way diminish or compete with his love for my mother. She would always be his first love and the parent of his children. Jean was his extra love in his life, an unexpected bonus, and he would always say how very lucky he was to have had two amazing women in his life and to have experienced a great love twice.
He never forgot, or substituted my mother, indeed he always kept her ashes in his 'office', and kept every treasured memento of her and photos just as it always was around the house. Jean was a bonus, and also wise enough to realise she was no substitute either - his home remained largely unchanged of all the trinkets of my mother's time, but Jean's presence was added - the flowers and the artwork, the new paint on the walls and curtains (needed) were her forte. We'd often get the photo albums out or chat about some aspect that would have interested my mum. Just because he was in a relationship with Jean didn't detract from the first great love of his life.
They didn't marry, and although they did live together Jean bought an adjacent home it meant they were in and out of both but it meant a clear financial divide, as they realised the inheritance issues would be too complicated for shared finances (her children had 2 different fathers), which was a blessing too.
Yes it took time to adjust, but once we realised how happy Jean made our father we agreed with his view: he was indeed a very lucky man, and Jean most definitely was a bonus in his life, and absolutely not a substitute for our mum. For all of us, not one of 5 living within an hour and a half of our dad meant it was one less thing to worry about knowing Jean was there for him day in day out, and that they had a happy and fulfilling life doing things together. For our kids many of whom could barely remember our mum, it was an extra old person to entertain the grandkids and made it much more fun for them. (exhaust one and you still have the other to wear out). Even so, our mum was never forgotten. She was Grandma, not Jean who was 'Jean' or 'Jeanie-Nana' (because her grandchildren called her Nana and were often there same time).
I'm sorry for your loss, but I hope my experiences will help you in resolving your difficulties in accepting your father's new friendship. Yes he is lonely without your mum, but I am sure this new friendship is not an attempt to replace your mum - as your mum will be the first lady he loved, married, and had a family with, something the new lady cannot ever be or do - but to replace his loneliness. Likewise, you are his child, and your children his grandchildren. The new lady will never be the parent/grandparent. That's your mum.
I hope you'll be able to see the new lady as a bonus in your dad's life, and in time I hope a bonus in yours too.
I do completely understand how much you're missing your mum though, I wonder would getting some grief counselling help you perhaps?