Like the first poster, I altered my down-time arrangement. Not because of another child, but because a fight sort of negated the whole idea.
Down-time has become many different places/activities in our house depending on whether it's down-time my son has needed or time that I needed, and what was available.
With my son, being given a choice to PICK which rest activity (out of a selection of 2 or 3 constants and a couple others that would change every few months), seemed to do the trick. A few times he even opted for a nap. How's that for contrary?
Also at about 3 1/2 we started setting a timer. He didn't have to stop his activity if he didn't want to, but it gave him a good idea of the chunk of time that was expected.
If it's a little down-time YOU need, may I suggest www.Starfall.com? It's an amazing free online reading program and it has a strong tendency to absorb toddlers for hours if you're not careful. (There's only so many times I can read a page in a book before the irritation creeps in, and no matter how well we mask it, the kids always know. But the recorded voice on the website is just as excited the 700th time they click on "A"!! "ASTRONAUT" baum baum bum baum baum bum!! "A" !! as the first. Even though it's designed for K+...it seems to have better results with younger children. Most of the 2 year olds we playgrouped with were reading by 3-3 1/2 and stayed interested in the site until they were approaching 5. On the other hand...most kindergarteners I know get irritated by it.
I would like to add at this point that I am in no way affiliated with Starfall,& I'm not advocating an electronic Mum...but we had the Terrible Threes at my house...and it helped save my sense of ahhhh. Side benefit, of course, was that my son DID end up reading pretty early.
Best of Luck!