One sec I'll replay the game and see if I can help. I'll post when I get to that point.
To start I do have the quick progress and skip minigame in the options section.
Also if you like this game you should try the chilly mod for this game. It's a stand alone based on an earlier version of the game but the story diverges alot and there is more content overall.
OK here is what i did day by day to unlock that area. ( what you need to focus on is all the Neala interactions and probably the last part of this partial walk through.
day 1
Morning
got money in couch,interacted with DIY locations in room, got phone, got med cabnet key, took picuture of mom and interacted with her again in the shower for points.
Leave out back door the exit map to the righ to go to hospital, talk to nurse.
Went to school talked to teacher, got picture and talked to her again. Went to cafeterria and got phone numbers on table. Went to class, (payed attention)
Noon
Talked to fred to once to sell pictures to danny, and again to find out where to get DIY tools. Sell 2 pictures to danny. Then go to class, ask for help.
Afternoon
Go to Kaylee store, talk to her, ask if she needs a hand, buy 4 DIY tools (i know you need atleast this many for the moment).
Go to park, talk to lost girl, interact with the bathroom door. Go to the fisherman shack and talk to the fisherman twice to get the bathroom key. Talk to Sara twice and Lisa once to get Lisa's info. Drop off lost girl to Kimberly at playground.
Go home and talk to mom to get another picture, then ask for money then tell her you are having pain. leave out the back door and talk to the girl next to her house. Grab number on dining room table. Talk to Ms Amos twice. Play hide and seek with Alison and hide in upstairs closet. Go back home and go to second floor bathroom and open medicine cabnet. Talk to sister's friend Dizzy. Go to your room and use 2 DIY tools on the floor then pass the time by reading or computer.
Evening
Go to sister's room and interact with the bottom right corner of her bed to get her key. Go downstairs and talk to Dizzy to find out she works at the bar. Copy sisters key at Kaylee's shop and put the key back. Go to the bar and talk to her and then give her a hand.
Night
Go upstairs and look at hole going into sisters room, go downstairs and catch sister watching TV. Go to bed
Otherworld
Jump in hole, touch Stone Glyph, wake up.
Day 2
Morning
Take picture of sister now that you have key. Repeat shower, nurse (talk then pain to unlock home visit), Kaylee (when you help her you have to go to appartments 3rd floor)
(as you leave home you'll go through scene where you first meet Neala)
Go to residental area and look through window. Go to school talk to Teacher go to class, attend gym.
Noon
Go to class, ask for help again.
Afternoon
Talk to teacher, Talk to Sara then Lisa, Talk to Kimberly then Amanda, hide next to bathroom.
Go home talk to sister get photo, talk to mom. Go see Ms amos, talk to her again. Go upstairs to your room to see your computer being broken, go see Kaylee to get a powercord, fix your computer, enjoy some "me" time. Talk to sister again about going outside, go upstairs and interact with the computer to find your sister then use your computer again, Go to bathroom, text sister, Go upstairs write love letter, deliver letter, look through window. Pass the time.
Evening
Go see Ms Amos then go to bar talk to Teacher, Dizzy talk and help to get number. go home and look our your window. Go to Sleep
Otherworld
Meet Neala offically. Solve puzzle wake up
Day 3
Morning
tell mom you got pain. Go to shower ask to join.
Go to resedent and see Sara.
Go to apartment and see Neala (should unlock next level in otherworld)
Go to school talk to teacher go inside school and defend Amanda, go to class. (talk to fred)
Noon
Sell pictures and learn about PayMeOn, go to class ask for help.
Afternoon
Talk to Teacher, go to cafe talk to Neala, Talk to Kaylee and work for her (chance to record conversation to blackmail her). Go to Park, look for Amanda, talk to Sara twice then Lisa. Go Home talk to mom and Ms Amos. advance the time by going to the bar and talking to dizzy then asking if she needs help.
Evening
Go to bar talk to teacher and then help Dizzy with work.
Night
Get a text to go see Dizzy. Go home look through sisters DIY hole and talk to her, go to bed. Mom night event.
Otherworld
Talk to Neala, solve 4 puzzles get ability to manipulate dreams glyph(top right puzzle) then get invisibility glyph. wake up.
Day 4
Tell mom youre sick to get nurse to come. Use invisibility to get past sister to take shower with mom. Go see Ms Amos Go see nurse about your "pain" Go see Neala talk to and then TF her.
Use invisibility and sneak into Sara's house to steal the Tape. Go to park and give tape to Lisa.. Go to school talk to teacher then go to bathroom. Teacher and Pricipal with have a fight about husband, talk to kaylee. Leave school go to Kaylee's shop. Go to class
Noon
Use invisibility to get picture of teacher and hear conversation while changing. Go to grocery store and talk to ms amos. go back to class ask for help then see her after class.
Afternoon
Talk to teacher, go to cafe talk to neala. Go to park get into fight with thomas, go invisible and talk to sara. talk to Lisa then go to bathroom.
Talk to Kimberly then Amanda then go hide in same spot.
Go home and talk to ms amos. then talk to mom about stickyness then help her out then take shower. talk to sister then advance time.
Evening
Talk to ms amos, have dinner.
Night
Use dream touch on sister and mom. go upstairs and peek on sister use invisibility and go downstairs. go to sleep. mom night event 2.
Otherworld
Left side is unlocked. talk to neala and do her event.
.....
the right side is still locked but if you go to her apartment in the morning and do her new scene then go to the park at night where the fisherman hut is and you'll see her selling drugs talk to her and another event will happen. then go to the otherworld and it the right side will now be unlocked.