Yes, the planets would be a lot smaller than your dots.
You have it right. See the map that is essentially the same as yours at:
this web page
It's dots are also way off scale, as is necessary for them to be visible.
Yes, Jupiter is much farther away than the Earth, but they are both very far away, so the absolute difference in size from parallax between the two isn't that great, because the effect of parallax isn't directly proportional to distance. Also, Jupiter is a lot bigger than the Earth.
PvK