how do I start the relation with the mother?
I've somehow figured out how to do it with the dad, but not the mom :(
That depends on if your character is feminine or masculine. If you are feminine, you have to have at least 5% femininity and start the storyline with your mom first, which just has you do a couple things with the both of them before you start raising your relation with either of them. If you are masculine, you should just need 5% masculinity and be able to start talking to her. Especially if you've already started the dad relation stuff, you should have interactions with the mom too.