You're in wonderful position to have you sister's trust during this trying time in her life. She must feel very comfortable with you. At the same time, you're in the
difficult position of being a family member she wants to be around more than others. Give yourself lots of credit for being sensitive to the delicate relationships right now, and for wanting to help. Major surgery is exhausting, as I'm sure you realize -- physically and also emotionally. It sounds to me like your sister hits her "outside stimulation" threshold when your other sister and mother are around. Who knows why this is. It could be linked to their personal histories. Or maybe your sister and mother are "too" caring, too concerned right now, which is wonderful, but can feel like pressure to a patient who is trying to rest.
So, what can you do as the sister in the middle? I'd start with some gentle face-to-face honesty with your mother and other sister. Explain to them that your recuperating sister appreciates their presence, but has shared with you that she feels fragile right now and easily overwhelmed, even with family. You can say that she doesn't want to hurt their feelings, and has asked you to intervene. Start with some suggestions, like cutting back on visits, or making them one-to-one, and no groups. Ask for their input so they feel part of the solution. You can stress that as your sick sister gets better, she'll probably welcome more attention, but for now, she's asked for a slower pace.
If this discussion doesn't go well, or is too difficult for you, there may be a hospital social worker who can help. Ask you sister's doctor for a referral. Hospital social workers are skilled at dealing with these exact kinds of issues. The most important thing right now is your sister's health. The feelings of your mom and other sister are also very important. But there's more wiggle room here, they can adjust and adapt more easily than your sister can right now. She has one main mission, which is to rest and heal. You may need to point this out, but if it's done in a caring way, they should understand.
I wish you the best of luck sorting through this situation.