I think you just might need a high affection with Kaali and you need to be the owner of Xavier's mansion to have her move in with you. To get to that point I think you need to do the following:
1) Have a cell built in your basement prior to confronting Kaali in combat
2) Spare her after defeating her in combat
3) Give her common clothes, a bucket of water, and a health potion (tomato juice works too I think)
4) During the quest where you're tailing Father Fox, you'll have to cross a broken bridge. To cross it, you first need to talk to Lui, the guy living in the woods who was sleeping with Kaali. You offer to release Kaali under his supervision, and he'll build the bridge.
5) Become the owner of Xavier's mansion (this is a separate quest)
6) Talk to Kaali and invite her to live in Xavier's mansion. I don't think you need a high affection with her to do this, but if you do, you can increase her affection by gifting her spears and taking her out to adventure with you.
It should be possible to reconcile with Alexia and Kaali through gifts I think. Alexia wants flowers, and Kaali wants spears, but I think if you just keep giving the same quality of spear, it won't increase Kaali's affection.
I think right now there are two furry pregnancy options if you include a scaly. The furry is Lydia who is found in the desert which is on the Eastern side of the world map, and the scaly, Liai, is found East, then North of the Swamp Village. Lydia requires NOT killing her, then completing her requests and also raising her affection through gifts and flirting. Liai requires first doing the Missing Oxen quest in the Swamp Village. Then in order to get the ox back, you can either negotiate and bring Liai meat or you can defeat her in combat. Liai is pretty strong for an encounter that's accessible in Chapter 1, so save beforehand if you choose violence. After getting the ox back, Liai's affection is raised via gifts, then flirting.