hm. A bit tangled, this one. Your dd has been brought up to think of of her absent, then dead father, all the time. I find it strange that she is still asking after him every day, to me this seems somewhat unusual, and not particularly healthy. Is there some part of you that idealises her father to the point of fixation?
For your bf, and I note you call him boyfriend rather than dp, this idolisation of a dead parent must be hard to take. He has loved and cared for your daughter for two years, and wants to be a proper dad to her, hard to do if you continue to hold up the absent, therefore, idealised parent as the ultimate in parent, which, by default, makes him feel inadequate.
On the other hand, its absolutely nothing to do with his mother, so that is pretty weird that she even feels ok to get pissy with you about this.
Is there anyway in which you are finding it hard to move forward and transferring this to your dd? Children need parents, and if you want her to have a a daddy now and in the future, then why deprive your dd of a real living parent, another daddy, if you will, who loves her as much as her real, first daddy?
Sorry to sound harsh, but a real live dad in her live is more useful to her in the long run than and dead, idealised version of a dad.
But that is all moot if you are not sure this man is the right man for you, and the right man to be your dd's new dad.
If you do become a family, then its only natural that she calls him dad, and comes to see him as her new father. That is healthy.
Only you can decide this.