Naps/sleeptime/overtiredness help

Hey Humans.

I'm having serious trouble with my 1 year old sleeping - at all, daytime and night time, she's never been a good sleeper since day one, I've been told it's a phase (a really damn long one), or teething (but no new teeth) or poorly (but no sickness signs), or sleep regression (do they actually have a start and finish?) and overtired (obviously) and at this stage I'm just at a loss.

My oldest (3.5yrs) was never a problem sleeper, he got straight into a routine and aside from regressions, he never had actual problems sleeping, even now he's amazing with sleeping.

But my daughter is 1 year now and I can not for the life of me get her to sleep or nap. Shes breastfeeding still, won't take a bottle or any form of other milk, just weak squash or breast, she has 3 meals a day and snack times. This is my 6th night in a row with no sleep I'm just waltzing around as zombie mum trying to get life done and I can't, we have a pretty strong routine with my son that we have tried getting her into but nothing seems to be fitting to work for her.

We get up at 6:30am, basic dressed bathroom, breakfast, we're out the house at 8:30 to walk my son to nursery, he's there for 3 hours, in that time I have played with her, we dance or sing, we've done book time, a bit of TV time, I've tried walking activities (she doesn't walk yet), or pop to the shop to do shopping- I drive there, note she hates the car and I mean she's screams when I have to put her in there and cries a good chunk while I'm driving so I don't take her out in the car if I can avoid it, and I've sat there in complete silence rocking/BF her but still no sleep or she'll go to fall asleep just before we have to leave at 11:30 to pick up my son. She's in a pushchair for the walk, so sometimes, she falls asleep, and I leave her in there to do so for however long she stays down which varies from 30mins to 3hrs, sometimes she's in there just angry with life and stays awake.

We have lunch when we get in at 12, she has hers later if she actually does go to sleep. I've tried a detour home with walking to try getting her to sleep in the pushchair but my sons had productive mornings and normally is tired from running around, hungry, thirsty and needs a wee so it fails miserably.

My son has TV time in the afternoon through lunch, then it's just background noise for whatever activity we do which varies but it's normally something we can all do -play doh, crafting, baking, sometimes we go for a walk around the lake and to the park, or I get things done I need to do house wise, then at 4 tidy up time and it's chill time for them and I prepare dinner. Dinner is normally between 5 and 6, then its baths (every other night as she and my son have dry skin problems), teeth and settle down for bed, normally for 7:30/8, my son is in his room we read books, he pops a film on and we cuddle and he falls asleep.

My daughter reads the books with us we've cuddled too, sometimes she gets jealous or frustrated and that's where it becomes a sleep problem for my son, and she starts screaming.

I've tried getting her down first, we've tried putting her in her cot in his room as they like the company, but now she's just waking her brother through the night. I've got in her cot to feed her to sleep but in the first hour she's awake, ive tried self soothing in her cot and she just cries to the point of sickness, I've tried her in our bed but she just fidgets and is up in the hour, we move her once asleep she wakes up, she falls asleep while being fed put her down she wakes up, in the odd moments my husband isn't called out and he rocks her to sleep the moment he puts her down she wakes up.

I've tried switching off in the afternoon after lunch to try getting her to nap and I have more chance of my son boredom napping which messes his sleep up than my daughter sleeping. She also overheats easy so I can't wrap her up to sleep either.

I spoke to the health visitor for her 1 year but didn't get much sleep advice just told to look at a website which has proven as useful as Google. I'm at a stressful point and my husband is starting to lose it as his time with us is little and its spent with screaming nights and dreaded days off of a miserable baby. Has anyone got any tips or tricks that they used, it's not a phase the girl is honestly tired and miserable and so is the rest of the household and neighbours now... Is there any help?

Is there any hope..?