There will most probably be time for your mum to get there, if you decide that you want her there.
This is your decision, you will be the one giving birth.
In the past birthing was mostly a female-only affair, with experienced women (mostly mothers themselves) supporting the birthing mother, and the father waiting outside the room.
In theory it's a good thing that fathers have become involved in the process, if the father is able to be supportive to his partner, it is of course wonderful for him to be present at the birth of his child. However, fathers shouldn't be insisting on their rights at the expense of the needs and wishes of the mother. He does not have an equal say.
"I think DP worries about her taking over since he doesn't know much about childbirth or babies"
Has he (or is he planning to) read any books about pregnancy and childbirth? Will he be attending antenatal classes with you? He can certainly educate himself to support you as best he can. However, it's not a competition between him and your mum. If she is able to support you as well, that's a bonus. If he's worried about "competing" with her due to his huge and/or fragile male ego, I would not be too impressed.
FWIW my mum wasn't there when I gave birth (I didn't think I wanted her there) but I wish she had been. I cried with relief when she arrived (shortly after the birth). DH did his best but in hindsight I would have appreciated her being there too.