When it comes to common courtesy and being polite there is a question of what's proper or appropriate. I don't think there's any etiquette book that would have a solution for your problem - this is not about what's appropriate but about feelings and emotions - yours and him. And the two of you would have to find a way in which the two of you will be happy.
Communication is the key here, I don't think you should demand that he get rid of the ashes, however, i think that in him marrying you, he did made a deceleration of commitment to your marriage which means that you are his wife now and not his former wife, and his main concern should be with your emotions and not hers. I think that it's totally OK to ask why he feels that he needs to have the ashes in display where it is and see if maybe his explanation makes you feel better about things.
Is what bothering you is the ashes or the thought that he might not be over his dead wife? Maybe finding out that there are other reasons but his sorrow about her death - maybe it's out of respect, maybe he made a promise to her, maybe it's because of their kids - there can be al ot of reasons.
I think that if you can bare the ashes after the two of you talked about it, then you should, but if that's unbearable to you, I think it's pretty reasonable to ask him to remove the ashes to a different, less central place in the house.