Depending on your kids‘ ability to pull or carry their own luggage / backpack, you might want to look at hotels near the Westlake Center in downtown Seattle. It has a station for the light rail, which runs from the airport. It’s a couple of dollars per person, has a luggage rack, is very clean, and runs all day.
I was in Seattle in September pre-cruise and did this. Then I walked around downtown, going to Pike Place Market and other sites. I used an Uber to get to my ship (It used Pier 66, so I don’t know the cost to Pier 91). I would imagine a timeshare large vehicle would be the best option, unless you can find a hotel with free shuttle to the port.
Seattle is definitely an eye-opener if you are not from a large city. But I travelled solo and did not feel unsafe.
I find Seattle hotels to be on the expensive side, especially during the cruise season. (That means anything over $200 for a one-bed room). Southcenter (Tukwila, about 5 miles from SeaTac, are often better prices, but some do not have shuttles). And if you want to do any sightseeing, you will spend at least 30 minutes each way in travel.