I'm from India and can say some interesting facts about hoe teenagers think as I am 21 now.If ur daughter fights with your brother why did u speak out for your girl,because she expects it.Apart from that u asked an angry teenager who have no faith, trust something like that over family to leave the house and so she did.As you said u don't have anyone to look after you,you should make a bond with your only existing blood relation your daughter.I feel that you should call your daughter to home or you both can have a private trip(only you two).In the trip or some lone time at your house talk with how important is she in your life.Tell her your feelings, about how great you feel about your daughter.
I recommend to stand up for your girl all the times she need and she expects it.
I hope you two will have a great bonding as a mother and daughter in future.
Making and breaking of relationships is always in ones hands.
Hope you make a great, enjoyable life with your daughter.