is this emotionally manipulative?

me and my mother have been having some problems for a long time. she basically uses me as a replacement parent for my sister and ive been having complaints about this for a long time.

recently she blew a fuse because i didn't want to pay for a take out. keep in mind that we agreed we'd go fifty-fifty on it before i started making the order(this would include her and my sister's food and mine). even within that 50/50 split, i'd still be paying for a decent amount of their food and not just the pizza i wanted. she got mad at me for not wanting to pay for the whole meal, saying i was selfish.

i only wanted the take out because there was nothing for me to eat in the house and i didn't want to spend the money anyway---she's forcing me to move onto campus next year and won't support me financially, so I'm saving as much of the maintenance loan i'm getting this year for that. in the end i just didn't eat anything for the coming 2 days, which that one take out would have solved, and she knew that.

spending £12-15 was something i was willing to do but the £30+ just was something i wasn't willing to do especially when i had to leave money in my account for the deposit for the accomodation she's making me get. i didnt even want to stay at home for uni---she was the one who made me do it. so for her to turn around like this is incredibly frustrating to me.
this happened a few days before christmas, when she ignored me entirely despite my attempts to talk to her and say good morning. she and my 5 year old sister left the house and left me alone the whole Christmas day where i just sobbed on my own for hours on end. No one had spoken to me for the whole day, my sister had opened my gift for her but assumed it was from my mum so she hadn't said anything about it to me and i hadn't been given anything at all. my mother was avoiding the gifts id gotten for her like the plague.
i attempted to give her the gifts i'd gotten her again on boxing day but she yelled at me so i left it.
my mum continued to ignore me until my sister's 6th birthday. every year i make my sister a birthday cake from scratch, and as i was making the cake she was suddenly very cordial with me and was very forthcoming about asking me what i needed for the cake and how much i needed, and when i went out to the shops to pick things up she was once again very happy and friendly with me when she was asking me to pick up a ridiculous amount chicken nuggets for the party and carry it home by myself for the 20 minute walk. again, during my sister's party she was very friendly to me when she left me alone to handle all the table setting and greeting all the guests for 45 minutes, and also as i lugged back the tons of stuff we'd brought to the part back to the car and during the 3-4 hours i spent making party favours for my sister and her friends.
the minute the party was over she went back to treating me like i didnt exist and being really snappy with me.
two days ago i attempted to give her the gifts again, she'd been ignoring me once again and she started screaming at me saying i was tearing the family apart, and i just stood there dumbfounded because i didn't understand her line of thinking and this led to more screaming.

shes being kind of horrible to me until she needs something, she wont speak to my sister if my sister is speaking to me, and because of this, i end up taking care of my sister for hours and hours on end when i have work to do because my sister gravitates towards me and my mother refuses to interact with her in these situations. if I voice any concerns about this to my mum just calls me selfish, until she needs me to pick my sister up from school and then she'll start being nice to me again for the day.
is this just regular unfairness or are these actions emotionally manipulative?

I would say she's trying to manipulate you. What sort of mother neglects her child and then neglects another just because two of them wanted to bond? She sounds immature. She probably doesn't even see you as her child if shes treating you like a parent and a stranger. I'm so sorry

Your mother sounds like a highly manipulative, extremely toxic, parasitic and selfish individual.
Parentification is one of the most appalling types of non-violent child abuse.
Don't give your mother another penny of your money for anything EVER.

Does your sister's father live in the same household or pay child support and have regular visits to see her if no longer in a relationship with your mother?

she's recently started making me pay for half of the bill for having a cleaner and for my phone bill which i don't really dispute, i think that's fair but i feel like she's going to start adding more to it

my mum had my sister with the intention to not have her father present, he has no interactions with her and neither does any part of his family, he doesn't pay child support either