Hello and welcome to JustAnswer. Please note:This is general information for educational purposes only and is not legal advice. No specific course of action is proposed herein, and no attorney-client relationship or privilege is formed by speaking to an expert on this site. By continuing, you confirm that you understand and agree to these terms.
I am sorry to hear about this situation. Unfortunately, I do not have good news here.
Under PA's landlord/tenant code (see HERE), there is no right to a family member to come live with the tenant. The closest that comes to this is that tenant may have guests:
"The tenant also shall have right to invite to his apartment or dwelling unit, for a reasonable period of time, such social guest, family or visitors as he wishes so long as his obligations as a tenant under this article are observed. "Section 250.504-A.
However otherwise, one cannot force the landlord to accept a second tenant/occupant without them agreeing.
Now, you do mention that the landlord stated that she can come live with you. However, the problem is that if there is a verbal agreement/discussion and a written contract, the written contract controls. This is called the parol evidence rule, so here, the contract controls. If it specifically says that no one else can come to stay, then it is binding regardless of what was verbally promised.
Now, the landlord is free to agree to amend the lease contract, but this is at their discretion. They may agree, or they may agree but may request a higher rent, which they can also do. It never hurts to ask/negotiate, of course.
Please note: If I tell you simply what you wish to hear, this would be unfair to you. I need to be honest with you and sometimes this means providing information that is not optimal. Negative ratings are reserved for experts who are rude or for erroneous information. Please rate me on the quality of my information; do not punish me for my honesty.
I hope this helps and clarifies. Please use the SEND or REPLY button to keep chatting, or please RATE when finished. You may always ask follow ups at no charge after rating. Kindly rate my answer as one of TOP THREE FACES/STARS and then SUBMIT, as this is how experts get credit for our time. Rating my answer the bottom two faces/stars (or failing to submit the rating) does not give me credit and reflects poorly on me, even if my answer is correct. I work very hard to formulate an informative and honest answer for you; please reciprocate my good faith with a positive rating.