From what I understand, if you have a movement preverb + something like ül or áll, then it indicates movement to a place that finishes with a state represented by ül, áll, etc.
"movement that finishes with sitting" is usually "sit down" in English; the nuance of "movement UP/HERE/THERE/ACROSS that finishes with sitting" gets lost in translation.
"we sit here" would be itt ülünk (location).
Perhaps "We come over here and sit down" might be a bit more precise for ideülünk, if you want to distinguish it from leülünk which is merely "sit down"?
I think "We sit here and read" should be accepted. English does not do as good a job of distinguishing between moving and still verbs as Hungarian does. "We sit down here" does tend to indicate the movement in this example, but "sit" is exceptional in this usage.
The more literal translation would be "We sit to here and read", although of course this is not correct English.