Some will not survive, some may make their way outside. If you can get a picture of one you catch in a container, reasonably close up, then you might be able to get an ID over on arachnoboards.com, which would help gauge the size they get to. Bear in mind the ones you're seeing aren't the 'baby' babies - they've already had, likely, 2 molts at this point. So they may not get very large.
If the environment is right and a spider is ready to make a sac, they will. Outdoors it follows the climate, but indoors we adjust ours so they'll adjust in kind.
Your spiders will spread out, and of those that make it to adulthood, the males will likely be the first to mature. Its theorised that this is to minimise sibling pairings. They'll then go looking for mates, so if still in the house they'll probably leave anyway in their search. Any females then will mature and need decent food stores so may move to where food is most abundant. This may be around plants and such.
None of this may be comforting, however I've always found learning more helps to reduce fear associated with the thing in question. They do spread out, and sacs have many in order to combat the fact that many don't survive to adulthood.
You could use this opportunity to teach your daughter how to manage her fear, and try to manage your own at the same time. They aren't a threat to you, and they manage flies - which can bring illnesses and crap. They're immensely vulnerable to us, we can easily squash them. However they're also super important parts of our ecosystems, and often specialise as per the microhabitat they live in - there are habitats with huge varieties of spider species due to this, each only capable of living in specific areas. Due to where they sit, as both predator and prey, they can be fundamental elements of these habitats and directly related to the survival of other species. They are really very fascinating, and close ups of their faces often look adorable, or pretty goofy. Jumping spiders are good ones to look at. This is just a suggestion. I would say trying to get a clear picture, and seeing if arachnoboards.com can help with identification (put under True Spiders and other Arachnids), or another relevant site or FB page, could help at least assuage your fears regarding the size they may reach.