I am in your exact situation right now (working at home FT too). Some thoughts:
Could you afford to still send DS to nursery a few half-days a week? We do this and it's great b/c DS loves it, DH gets some time off, and I get a quiet house.
Is it at all possible for you to take work elsewhere -- even just to the coffee shop for a few hours? I think the hardest thing about this setup is that you are there, but not really there. I know my DH finds it really difficult and I would give anything if it were practical for me to work elsewhere, it's a rotten setup.
The only way it can work is if you really resist every urge to go out and intervene. I know it's hard when DS is crying but you have to let your DH get on with it. Imagine if, when you were on ML and learning your way, you had someone in the background as a constant potential source of correction. It would be really stressful and unpleasant!
The phone thing would drive me nuts. I think it's pretty bad form. At the same time, there's nothing wrong with your DS playing by himself for a while either. If you can get them out of the house more, a little phone time will probably seem less annoying.
Finally, I think instead of pushing set activities, you should just agree that certain blocks of time are Out of House time. Then keep a list or schedule of potential activities and errands! handy and let your DH decide what he feels like doing.
I sometimes just take DS for a two hour walk around town. You don't need elaborate activities, the point is just to get out. If you make it sound like he needs to come up with really amazing and great things to do, he might be less inclined.
I really would let him find his own way with things, even if it drives you a bit nuts.
But is he happy with this arrangement? Tbh I'm kind of surprised a teacher is having trouble coming up with structure and activities and fending off boredom.