Hi Noheroicsplease,
this is a really horrible symptom & has been one of the hardest for me, from the start of peri through to 5 years post-meno where I am now, both with & without HRT. I do wake with night sweats & have a chronic pain condition that disrupts sleep, but also wake for no apparent reason as you describe & then seem to be too alert to get back to sleep. This can mean lying awake for several hours, usually after about 3:30 am, which seems to be the time my body can't reliably sleep beyond. Kathleen's jet lag analogy is spot on. I have enough books on insomnia to stock a small library but I'm sorry to say have yet to find the answer!
That said, there may well be something that could help if you read around, assuming you haven't yet had time/energy to do this. If you haven't tried progressive muscle relaxation, some people find this helps them get back to sleep. Starting at the feet or head, concentrate on relaxing each muscle group as you progress up or down the body.
Focusing on breathing, as described in meditation programmes, also helps some people - probably because it's so boring!! Meditation itself, when practised regularly is said to promote restful sleep, but I imagine with a busy life and young child, finding time for this might be very difficult. There are audio relaxation exercises & meditations specifically for insomnia that you could listen to on an MP3 player when you wake, without disturbing anyone else.
Some people also find that a balanced calcium-magnesium supplement, the sort you take for bone health, can be very helpful, if this is not contraindicated for you. There was a TV programme a few months ago in which Michael Moseley also conducted an experiment in which he found regularly taking Bimuno before bed (GOS powder sold as a prebiotic for gut health) really helped his sleep.
I agree with the suggestion to try switching your oestrogen to early morning & the mention of lavender is another helpful one. I do hope you find a solution & please let us know if you do - I imagine many of us would be very interested!