Ziva and/or Caleah been pregnant doesn't affects Alice's quests.I restored the temple a while ago and every time I've gone back there there wasn't any new quests. I've done mass a couple times but haven't been able to get ziva pregnant which i think is by design. got the swamp girl pregnant though. For the tower I just finished Ancient Technology and havent hatched the egg yet.
If Alice goes to fetch the MC at night when he sleeps in the inn, there shouldn't be a problem for the carriage to appear.
Even if you can't trigger the carriage at Weirdwood, Alice will ends up at the Temple after you start making Wine at the Family Farm.
She gets kidnapped and after you rescue her she can start her training as an Acolyte.