First of all, ‘hate’ is a pretty strong word. I think the word you really want is ‘resent’. Resentment happens in relationships from time to time.
You resent your sister for getting away with being a lazy, drug-using slob. Fair enough, but does it actually hurt you? Or are you simply just letting it get to you because you know what she’s doing is wrong and you wish she would stop. If you actually hated her, you truly wouldn’t care what she did. Do you resent her because she doesn’t look after you in the absence of your mother?
I think you resent your mom for leaving for days on end. I get this big time. You certainly sound young enough to still need your mom around. She sounds like she expects your sister to step up and play mom when she’s not there and it certainly does NOT sound like she’s doing that. So, you end up resenting both of them. This makes sense and you’re not a horrible kid for feeling this way. You sound like a very normal kid to me.
If you haven’t spoken to your mom about how much you miss her when she’s gone, you should. This doesn’t make you a baby. Tell her about the practical stuff that makes you miserable and sad, because your sister isn’t stepping into the role and responsibility your mother expects.
Maybe you can sit down with your mom and sister (and a school counsellor perhaps?) and work out who is responsible for what you your mom leaves. If your sister is given certain things to do and doesn’t do them, then she can be held accountable and you’ll have something very legitimate to bring to your mother, rather than sound like a ‘tattle-tale’.
‘Stuff’ doesn’t get done by itself. There’s cleaning and laundry and meals and shopping and when your mom is gone, the structure of the house and routine goes out the window and it can leave a kid feeling pretty insecure.
I don’t think leaving is the answer (depending on your age and if you’re trying to finish school..), but perhaps trying to learn to be more independent and creating your own routines that make you feel safer and more secure. If your sister is meant to buy the groceries but doesn’t, start insisting that your mother give you half of the grocery money so you can buy your own food and cook your own meals. Learn to do the laundry and only do your own. Make sure you clean up after yourself, so when your mom returns, she can see what a slob your sister is and perhaps your mom will give her the rev-up she needs.
I don’t know if any of this helps. I’m assuming an awful lot of detail, but I hope you work it out. Just remember… you will always love your family, even though you may hate some of the things they do. What you are feeling isn’t hate for them. Sisters grow up and change and parents are only human. Having a good talk with someone and/or your mother might really help.