My 2.7yr old has a serious rage problem and I don't know what to do 
I spoke to the health visitor about it, and they sent me to a speech and language therapist (she is pretty non verbal) who said she's probably just frustrated and signed us off.
She literally has fits of rage that can last between 40minutes and 2 hours, during which time she screams and tries to climb up my legs, hitting me; but when I pick her up she writhes around pushing me away.
The last two days it's gotten so bad that she is literally foaming white saliva from her mouth and dribbling it all done her shirt.
It's pretty much started since she dropped her naps, but she will not nap, and now wakes between 2 and 4 am most nights to have another one of these rages. We can't just let her cry it out as she shares a bedroom with her autistic brother and he needs to sleep, so we take her down stairs, but nothing calms her. She just spends a few hours writhing and screaming on the living room carpet and eventually falls back asleep 
She looks exhausted.
What can I do for her?