Hi Flojo,
I'm sorry for all the anxieties you are experiencing. I have been diabetic for 15 years and do experience night-time hypos. Nowadays, the VAST majority of these cause me to wake up and treat it with food, thank goodness. Whenever I wake up (even if it's clearly just to go to the washroom) I always take my blood to gain a sense of where my blood sugar is, and where my blood sugar is going... Also, when I am tired, I am a lot worse at picking up signs of hypos.
When I was younger, however, it was a bit of a different story. Sometimes my body would wake me up when I experienced a hypo in the night, but I have to admit that my poor mother did have the experience of coming into my room in the morning (sometimes in the middle of the night, when she came to check on me) to find me quite unresponsive/drenched in sweat/ having a terrible hypo. [in these cases, she would rub gluco-gel into the inside of my cheeks, or if I could swallow and talk, give me orange juice]. I think that most often this was due to the 'lag effect' of taking dance classes later in the night (7pm-9pm). I continued to decrease my insulin and, ultimately, ended up taking no long lasting insulin, but did still experience the odd bad hypo. Happily, today we have fast acting insulin etc. that helps to avoid most of these lows (I was only giving 2 injections back then and, thus, had to figure out my meal plan for the entire day). But I can definitely relate to you and your daughter's current struggles...
I would recommend eating protein before bed, in addition to the carbs Chloe is currently eating. When I was younger I would often have a piece of toast with peanut butter, and also experimented with lower-carb protein shakes before bed. For me, the protein helped me to get through the night. When my hypos were very low (and even now-a-days, when I am a little unsure about how I'll get through the night) I set my alarm to wake myself up a couple of times throughout the night in order to check my blood glucose levels. Of course this is not an ideal long term plan as it interrupts the sleep cycle, but it could help you to document her blood sugars over the night...
As for her going to 1.4 without recognizing - yes, this could be a symptom of a general lack of hypo-awareness. However, we must keep in mind that when kids at this age are going to school they aver very distracted - they worry about friends' impressions of them, teachers, gym class, notes to take in class, homework to submit, tests etc. Such preoccupations can lead to missing the signs... Even today, when I am really engaged in something I might not catch a low until a bit lower than usual. While I have just recently ordered a continuous glucose monitor (by Medtronic) for myself, it sounds like this might be a good option for Chloe. Also, 1.4 is dangerous, so talking to your team about whether there are steps to increase hypo-awareness might be a good step.
Anyway, sorry for the long message... Take good care. Hang in there, you are doing a great job!