Ileosa is assuming that she'd betray her own mother equally readily?
Ap-parent-ly she dodged a bullet that Eodred died without managing to knock her up first.
...If eventually having children is non-negotiable, what are the safest ways to do it? It doesn't have to be immediately, Ileosa's current plan was already to get her eternal youth and character levels and unchallenged despotism all sorted before taking on that kind of distraction.
Ileosa's first thought is that she could leave a hundred unacknowledged bastards to be raised by their mothers far away from Korvosa, and never tell them about their heritage. It's not what she really wants - she'd like to be a better parent than her own father, to apply what she learned from watching him and make him proud/show the old man up - but it'd be better than nothing.