what is the best thing that i can do for my mother?

You should not keep a secret especially to your mom. You love her yet you lied to her. The truth shall set you free as what an old cliche goes. Your mother has the right to know about the situation.
If i were you, i would tell your mom about everything that had happened especially to your sister. You cannot keep it a secret all the time. Tell your sister to go to your mom and ask for forgiveness. Thats the fact and you should accept it. I know your mom will be very dissapointed but keeping it as a secret to her would make her feel angry not just to you but your sister as well. It can only make the situatuon worse.

love her what else she needs from you.?

hi ahgie. I never thought you have problem like this. Well for me you should convince your sister to tell the truth to your mother. She can't keep that forever. Make your sister realize that she's just making things worse by not telling your mother asap. I'm sure your mother can still accept her for she's her daughter. You on the other hand may get some blame and rant(hala ka bwahahah)for not telling the truth to her. But it's alright. Pain will heal in time. I hope the problem in your family will be resolve in no time:)

i think you can give the flower to your mother and give some presents to her,such as clothes and cake.