I think the idea of pregnancy being "irrational and "magic" " is really particular to your game and your take on what the Apocalypse means. It's not at all how I've had pregnancy and parenthood show up in games so far, but if that's the sort of PC you want at the table, why not? I also kind of like the idea of there being a character class of Mother, independent of the sex of the PC. There are men I know who would make excellent Mothers using these moves.
I do think you could stand to adjust the moves down. The moves I think have the best potential are these:
Piece of Mother's heart: Whenever you go aggro or seize something by force in defense of one of your children, roll+weird instead of roll+hard. I like this because it hits the whole idea of a fierce and fiercely protective mother so well.
haec ornamenta mea: you got a small gang, your offspring and their friends (2-harm gang small savage 1-armor). I like this because the idea of a mother with a small horde of kids of various ages, willing to mess things and people up on her word, is potentially really scary and excellent.
Mother stare: you always roll+weird instead of roll+hot in attempt to manipulate. I took off the last few words, to make it apply to anyone not just her children. Because that stare works on total strangers :)
Everybody’s Mother: you can choose one NPC or one PC. You must pass some time together. With a NPC roll+Weird. 10+ you can consider that one as one of your children. The same on 7-9 but with string attached. On a miss he hates you. With a PC roll+Hx. On a miss he get +1 Hx, on success you can consider him as one of your children. On 10+ they mark experience, on 7-9 nothing. I'd drop the NPC/PC differences, and just let the roll+Weird stand. And I'd clarify whether this was something you could do more once per session.
Something to spare: every time your children are in need roll+weird. On 10+you got something valued 1-barter giving something important for you but without value (you can add other barter). On 7-9 you get something valued at most 2-barter, but you are in debt with someone you don’t like. I like the idea behind this, that a Mother could find resources from somewhere to help her children, but I think the wording is a bit odd. Maybe try: 10+ gives you a 1-barter item you've been saving against a rainy day - lucky for your children, and they better be grateful; on a 7-9, a 1-barter item you can use to buy off their need, but it has sentimental value to you; on a miss, you can get a 2-barter item, but it comes with strings attached to someone you dislike, and the MC will tell you what.
Dear Mom: if some of your children come to you to ask advise, if they do what you said they get +1 roll. I like this because it follows the Everybody's Mom roll so well.
Moves I'm not so into and why:
heart of a mother: at the beginning of each session roll+number of children (max+3). On a miss you hold 3, on 7-9 you hold 1, on 10+ you hold your breath. You can spend the holds at the beginning of the session or when the MC ask you to spend them . I get the point on this, to keep your kids safe and etc, but it seems like a move that really blocks some of the other moves, and it feels like it could put some of the prime motivations of the character off the table.
I can grow people: you get a pregnancy clock. This seems to be sort of the defining quality of the Mother - kind of odd to make that a move. Unless this is a particular +weird move for male Mothers ;)
Far from eyes: if some of your children (under ten years) is not with you or with someone you can rely on when you come back to him roll heart of a mother, but roll+how many hours you stay away (max +3). It might just be a language barrier, but I'm not understanding this one at all. Is it about keeping your young children safe, finding them, or how long you can leave them unattended?
Happy family: you have someone important you can rely on. It is a NPC, has his own life, but he can help you. Can be the father of your children, your sister, your mother or someone else. I see the appeal of this move, but I'm not sure it's that easy. Maybe you could sneak this in as a 7th move option, but I'd rather see you working that stuff out in play. Maybe another PC is your reliable person, or maybe that's a big thing at issue for you that I as the MC get to poke at.
Worn Out: you got -1 Hot (min -3) and +1 Weird (max +3) Ok, this one is probably my most personal objection, as a hot Mom of three kids :) But seriously, I'm not following the Worn Out idea here or in the proposed Heart of the Mother. The PCs are the only people in Apocalypse World who are NOT Worn Out, and to give that to a PC seems just backwards.
I do think your pregnancy clock is pretty good.