I have had Type 1 for 15 years and still sometimes struggle with night-time hypos. In particular, I struggled with them when I was a dancer and did a few hours of classes later in the day (say, 5-7pm) - this is called the 'lag effect': when exercise kicks in a bit later.
Anyway, I have learned to check my blood sugar before bed, and then 2 times in the night. When I was younger (and newer to diabetes) I would set my alarm for 3 or 4 am. Granted, this wasn't tough for me because I am a light sleeper, but also fall back asleep pretty quickly, so I understand this might be frustrating for most people. Nowadays, I drink a lot of water before bed to ensure I will wake up in the night to use the loo, and then check my blood sugars.
Reducing night time insulin is a good move (again, speak with a member of your team if you need help with this). At one point in my life I was giving 1 unit before bed and STILL going low. I ended up having a piece of toast and peanut butter, or a protein shake with fruit in it for some carbs, before bed. The protein really helped me get through the night.
Anyway, best of luck. I know from experience that night time lows can be very frightening (for you as well as your family/partner). Take good care and good luck!