Fair indeed.
Point still stands (at least depending on state) that without a residential lease agreement in the US then generally you would be considered a guest in your family’s house if over the age of 18. As such OP could be fairly easily evicted.
Depending on where OP is, that’s not strictly true. If you are in a situation such as this, at least within the UK, you are not strictly entitled to the rights of a tenant if you do not pay rent nor do anything in lieu of rent.
Basically in the UK if you do not have a tenancy agreement, cohabitation agreement, or license to occupy, then it can start getting very complicated. If they were named as a property owner, or had a common understanding of financial interest in the property, they might be able to fight for a stake of the house, but that isn’t really the point here. In the end whether they can be kicked out legally is a complex issue (at least in the UK) and not really a question we could answer here.
Informal tenancies seem to be state-dependant from what I can find (more concrete in california and florida), though I’d be fascinated to see if this has been legislated or litigated upon more generally. Of course verbal contracts are valid contracts, but that’s the sort of thing that would probably have to be sorted out in court.
In the end as advice for OP, I stand by the opinion that “they can’t kick you out without notice” is not a good idea to base one’s decisions on. You could be kicked out, whether it is legal or not, and the legality of such a no-notice kick out on a verbal and informal contract is certainly not an entirely non-disputed concept in all states.
OP could get kicked out, and maybe they could take their mother to court to try and get that solved eventually, but in the immediate they would end up houseless and in a pretty dire situation.