When I was pregnant, when I had to get up to pee, i would try to walk almost with my eyes closed and wouldn't turn any lights on because if I woke up, I would not get back to sleep. (Prior to being preggo, I almost never had to get up to pee in the middle of the night)
One thing that used to work for me with insomnia (pregnant or not) was something I thought of as "shutting my inner eyelids or closing my eyes twice". It's hard to describe, but when you just lightly close your eyes, like you normally would to go to sleep, you're still very aware of all outside stimuli and your brain is still firing away. When I would more completely close my eyes, it seemed to block out more of the light (even in a fairly dark room), and to close some of my runaway thoughts as well, even if, like you, I had no stress or worry that I was dwelling on.
One thing you cannot allow yourself to do is to start making a list of all the things that need cleaning or that you'd like to do IF you got a full night sleep, just one idea will start a whole chain reaction that can keep you up for hours.
Try to get outside first thing in the morning, enjoy that bright morning sunlight, maybe it will help reset your clock and stimulate your body's own melatonin. Maybe you could use this time to play with your son, or go for a walk.
Try to get your husband to take full responsibility for the dogs, let him know that you CANNOT be woken up or you will NOT function, which won't be healthy for you, your son, or the baby. Let the house go!!! And definitely get your son outside to play at least once each day, that was the only way I could handle my daughter's energy level at that age.
Good luck! Insomnia is very frustrating, and being over-tired leads to more insomnia, it's a vicious cycle.