I read this and it rang a bell. I'm thinking about HE the middle child on the basis that his two siblings are at school and I will have more time to concentrate on his academic progress because I'm not trying to deal with them in the day. If someone said to me I should HE all three I suppose I would think that defeated the point of giving him that extra attention...
But perhaps we are both looking at it from wrong end of telescope.
Maybe the sort of HE ng you are doing need to change to accommodate both your children and they will benefit from that. Maybe more outdoor stuff, less formal work. Learning through going to park, museums, shopping rather than writing stuff. More messy play.
In a way what you are describing is a set up where ds1 IS getting all your attention and it is not suprising that ds2 is probably playing up. But you could turn the freedom to get out and about to your advantage.
I have a friend who is a seasoned home edder and she found adding toddlers into mix an unexpectedly difficult because I suppose she was by that time used to dealing with a 8 year old who was happy to do more formal work, and she expected that of herself to be able to "teach" him, and deal with toddler stuff. But maybe there is a different way of looking at it.
I am re-appraising my own ideas about what Home Ed is (a sort of mini-school system I suppose I was imagining it to be) from your post. I bet you are doing a wonderful job with ds1 and some minor shifts could make the difference to ds2 getting a lot out of his brother being at home too. I think it will be fantastic for him to have his brother there, and they will learn more from each other too.