I am a SAHM, and had both my kids home, for a certain period after my daughter's summer program ended and until she started school.
I did things with them, but also, they had independent play too. I simply told them, I have things to do too, things around the house, and I cannot entertain them every single minute. It is the routine... that you do, that they will realize.
And, if my kids get 'bored'... well, that is good. Being 'bored' also forces them to get creative and problem-solve... I tell them that. I ENCOURAGE them to think of things... and they do. On their own. It take practice.
My kids are almost 4 years old, and 7.5
I have a routine with them... .daily. They know it.
I also teach them 'responsibility' and what that is... and that they 'help' in the house too, and it is not always 'playing' with Mommy being the entertainment center.
I know its tiring... but you can do it.
Verbalize, the day to them, what is going on, what they can do, what you need to do, and the routine... that is what I do with my kids. They understand.
BOTH my kids also nap... my eldest when there is no school, and my youngest every afternoon. It is a routine. They get tired, they nap. Otherwise, they are fussy and over-tired.
All the best,
Susan