It appears that on regular fares, children (2-15) are half the price of adults. Are you sure you are putting them in as "children" in the first screen? If you don't mind traveling in coach (as the_traveler mentioned above), adult round trip fare appears to be approximately $372 and round trip fare for children would be $186 each. That appears to be much more affordable than $1800! (Either you have a lot of kids or you were looking at a sleeper...)

Even better, a 15-day western region pass for the time period you're looking for (which falls under Amtrak's "peak" travel periods) is $369 for an adult and $184.50 for a child.

Go here for more information and here for the prices for passes.

So it appears to almost be six of one, a half dozen of the other for the railpass versus just booking the reservations. In that case, why not go with the railpass? That way, you can take other trains or connecting trains (say, from Los Angeles up to Sacramento to catch the Zephyr).

In any case, happy travels and I too send wishes for peace in your neck of the woods.