At wits end

Short version:
3 year old has woken up last night at 4 am, and tonight at 2 am, demanding TV, throwing fits, waking up 6 month old that is in a sleep regression Already, and waking up entire townhouse with thin walls and new neighbors . Give in and turn tv on so she shuts up and let's everyone sleep? ?

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Long version:

I am so depressed. For the past two weeks have been dealing with my 6-month old's sleep regression, where she won't let me put her down to sleep EVER. Only wants to be held. So I can't sleep deeply because I'm holding her in bed.
On the nights that my husband doesn't have to work the next day, he has been letting me sleep while taking the baby downstairs. I work three days a week so I am doing the majority of"night sleep with the kids" the Dynamics are that due to space, I room share with 3yr old and 6 month old. Dh sleeps downstairs . **(We are looking to move soon where we have a bedroom for the kids, so it is what it is right now )**

We Live in a townhouse with very thin walls- you can hear neighbors next door vice versa. Everyone's room is upstairs.

Twice in a row,
3'year old has woken up demanding the tv. Last night at 4 am, and just tonight at 2 am. When I say no , she escalates the situation to the point that she's tantruming, wakes up the FINALLY finally sleeping 6 month old, and the entire townhouse. Yesterday my husband swooped her downstairs and calmed her because I had work the next day. Today I worked, but as dh works the next day it fell on me. It is now 4 am and am hopeless. She wouldn't stop, throwing things around room. Saying she wants to go downstairs . Saying she wants to watch tv. That i am yucky . Tvtvtv tv. "I'm going to go downstairs then." Then makes to leave the room. Nothing I said stopped it , only escalated. Screaming , crying. Writhing around , throwing everything , looking for my phone so she could throw it. I know if I give in- she wins and will do it every night. But she's been doing this every night anyway!! I haven't slept in like 2 or 3
Weeks and am losing my mind .

I ended up strapping everyone in their car seats and driving around neighborhood at 3:30 am because the noise she was making and my horror of waking entire house (neighbors included ) was stressing me out . I can't do this on work nights tho . I don't know what to do !!!!!
Oh and after she finally calms down she gets mad that I'm holding the baby that she's woken up and says to put baby down in the basinette.

I'm not sure if this is a vent, or an "AM I ALONE HERE WITH THIS ONE??", or what. Do I just give in and put the tv on so she shuts the #%^* up and lets baby (and household) sleep ?? Ignoring hasn't helped. "Firmly saying no" escalates it.

P.s. We need the upstairs bedroom tv for when one of us (myself or dh) wants to come up for alone time. I guess I can maybe hide it behind a room divider at night? She will know it's still there tho. She also bargains for "downstairs tv" so I don't think having it in the room is the issue . She made to leave downstairs (where dh was sleeping) in her tantrum episode

Ugh my life sucks right now