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I am sorry to hear about this situation.
"My question: When signing a contract/lease, do both parties sign the same lease agreement? "
Yes. Unless otherwise specified on the lease contract paperwork, the signor and co-signor sign under the same obligations. The landlord can pursue the signor and the consignor separately or jointly for the lease.
"The other issue is they have rented my daughter a two bedroom apartment but the apartment complex showed, and made her pick the bedroom of a three bedroom apartment (bedroom "c" to be exact) as that is what she went to rent in this apartment complex."
It does not matter what apartment they showed her; it only matters for what she SIGNED. They likely showed her the public example that they do to everyone, and naturally it is one of the better models. However the contract description controls what she is renting. It is like test driving a higher end car model, but then signing a contract for a lower model - the contract verbiage controls. And it is presumed that the person read whatever they signed.
"What are my options if any?"
I am afraid that there are few. Actually, the company did describe them - the 3 you mentioned earlier. The fourth one is to simply walk away from the lease. However they will get to keep the deposit and may even sue for breach of contract. In addition, this can hurt both your and her credit. Ergo, this option is not recommended.
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