I don't know who legally owns the ashes(if indeed anyone can "own" them) but if it helps I can tell you what happened with my mother's ashes. The funeral director kept the ashes until we (my father and I) had talked about what we wanted to do with them - they said they'd contact us in a few months if we didn't collect them. Eventually we decided to have them buried in the garden of remembance at the crematorium, so collected the ashes and got it arranged.
I can only tell you what I would do if I was in your partner's position - If the ashes are still at the funeral directors, I would collect them and put them where I wanted them to be - I would not tell the "dad". There is nothing he could do about it legally, all he could do is shout about it, so be prepared for that.
Let us know how things turn out, I would be interested to know. I hope the ashes can be laid with your partner's mum.