itch.io

Yes, you need to send the child to the Artifact to have another from the certain mom, the gender of the child will be the same tho, also the same appearance. 

You can bring Madison to the beach when you increased her Love Level enough.

Someone already answered, but yeah, you didn't pay attention, only one kid per mother, the ones you send to the artifact pretty much stop existing unless you bring them back.

And the genders are set. The girls that give birth to boys will always give birth to boys and so on.
Same appearance and personality, basically it's the exact same kid and the only reason to send them to the nexus is if you have a preggo fetish.

Also Madison will only go to the beach if you have a kid with her.