Is a cat the right pet for our family?

I have been doing a lot of research for the past few years, trying to convince my mom that a cat would be a good pet for our family. She says she would't mind getting a cat if she didn't travel as much, though I try to convince her that cats are independent and would be fine not having human interaction all day for a few days. Normally for a few months every year (two) she is gone for 3-5 days off and on. And even when she is gone, my brother walks home to her house after school every day until my dad comes to pick him up a few hours later (our parents are split) so he would be there to re-fill the food bowl, and water, and provide some tlc. And then we normally take a few week long trips here and there, normally around Thanksgiving, spring, and Christmas/New years. But we have family, and neighbors that would kindly come and feed and clean out the litter box for the cat. Would that work, or not really?