What you describe is called gynogenesis.. The offspring has only DNA from its mother, but conception requires sperm from a male of a related species. The sperm triggers the egg to develop but DNA from the sperm does not become part of the offspring.
Gynogenetic females have to obtain access to sperm, but males do not
gain from matings with gynogens...
Theoretically it would be easiest for gynogens to obtain sperm from
males that release sperm for external fertilization. However, several
gynogenetic species have internal fertilization. Females require
intimate contact with males to obtain sperm. The Amazon molly uses the
two species that were involved in the hybridization, P. latipinna and
P. mexicana (Schlupp et al. 2002). A third host species, P.
latipunctata, has recently been described (Niemeitz et al. 2002). In
this case, the third host may have made secondary contact with the
Amazon molly only recently.
I think I have read of lizard species that do the same thing - all the lizards are female but to conceive they need sexual behavior - either with a male from a related species or from another female of their own species.
The linked article sets out the evolutionary conundrums that the existence of such species pose.