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Tenant law varies WILDLY from state to state. For instance I'm in NYC and I've seen friendships torn asunder by rental disagreements because 99% of the law is on the tenants side in New York. I saw one person literally wait out an eviction not paying rent for nearly two whole years, thats how long it took for the system to remove him from the property. One subletter was written up in the New York Times for taking over the apartment for over a decade (agreement was for a year) as the nightmare tenant from hell.
In other cities I've heard that eviction and legally having stuff removed can happen start to finish in as little as two days.
You may have been naive letting them in to the apartment in the first place, but they are doubly naive thinking that they can just waltz in and legally take over the apartment.
The landlord has the right to vette any prospective tenant, if their credit is bad the landlord is probably under no obligation whatsoever to sign a contact with them. The landlord may not want to have his/her/it arm twisted into a contract period and this new happy family might find themselves being evicted either way. Or they might not. If I were you I'd contact my landlord and spell it all out in gruesome detail, your landlord may disagree with your roommates, and if that is the case then you are no longer the one with the problem
I agree with all the other letter writers who said that whoever's name is on the lease is the one that has all the power and the liability (unless you live in NYC, in which case, you're all royally screwed).
Call a lawyer. And stop feeling bad about this.
This couple is trying to make their problem (a need for privacy and more space) into your problem. They are the one's with the problem, if they had approached you asking nicely you probably would have tried to work something out with them since you seem like a nice reasonable (if not a little gullible) person. They've made it hostile, and giving you an informal eviction notice suddenly with no financial help is DAMN hostile.
They seem determined to make their own problems bigger than they need to be, I don't see any reason why you should stand in their way. Baby or no baby, the only way these kids will grow up is if they face consequences for their behavior.
Find out what your liability is before you act, and base your actions on that.