OP, if your mum told you to take things and what she'd like you to have why, months after her death, hadn't you done it? Why hadn't you taken her jewellery to remember her by? Or was your dad somehow supposed to understand that it was his job to keep it all until you were ready?
He seems to understand you rather better than you do him. He kept his new relationship from you because he knew you'd be upset – and he was right.
It's not that I'm not sympathetic to you – my own mother died some years ago and I know the hole that leaves in you – but you seem to be adopting a very passive role in this. It seems to me as if you've done nothing pro-active and you're just kicking out at what your dad is doing. It's childish, teenage behaviour. Your father has his own life and it doesn't revolve around you. You need to grow up and acknowledge this. He's getting older and if a chance of happiness comes his way why should he refuse it?
Is there stuff getting in the way for you? Did you have a complex relationship with your mum or dad or both? Are you projecting your own stuff around your mum onto your dad? I ask because a friend of mine who'd had a difficult relationship with her mother and had been quite unpleasant to her in the final years of her mother's life seemed to transfer her anger onto her father after her mother's death. Your response is striking a similar chord with me.
It took my mum more than four years to die of cancer. It was a long, long time for my dad to grieve as he cared for her. He lost his old life with her long before she died and was ready to move on within a year of her actual death and I can understand that and imagine my mum approving.
Be an adult. Book some sessions with a bereavement counsellor (there are often free or highly subsidised local services available) and work through your own stuff around your mum's death. Go with your siblings and take what you want from your mother's belonging. Ask your dad and his new friend out for an informal pub lunch or similar and get to know her. She's not going to replace your mother and who knows, she may be a good thing for your father and for you.