I did the trail counter-clockwise from Timberline lodge with my wife last September. Strangely, we met very few people going this direction around the mountain. I have no idea why that was because it's a fantastic way to do it. You avoid the crowds, you cross Eliot Creek (the only real obstacle) earlier on in the hike, and you end with Paradise Park. Additionally, the views of the Washington volcanos are spectacular heading north on the east side of the mountain. The east side of the mountain was easily my favorite stretch of the whole trail.
We took the "ropes" route across Eliot Creek and I didn't think it was all that bad. I was expecting something much worse. Definitely do the crossing as early in the morning as you can though. We crossed at about noon (which wasn't ideal), and the flow rate significantly increased during the hour and half it took us to cross the entire valley, down and back up.
There is no way around crossing Eliot Creek if you want to circumnavigate the mountain. You are either crossing at the glacier or fording the creek a bit below that. There is no better crossing downstream and no bridges to speak of that can be easily accessed by a Timberline Trail hiker. It's a bummer, but that's the situation.
As for taking kids across Eliot Creek. I think it depends on the kids and depends on the flow rate at that time. The water is truly ice cold and can be anywhere from shin deep to above your waist, depending entirely on the flow rate and where exactly you choose to cross. The cold water will be a factor, for both kids and adults, but more so for kids and their higher surface area to volume ratio, so don't overlook that. It's certainly not a trivial crossing, so I'd just be careful if there were kids involved. You can always turn back if it's too much.
With that said, the crossing basically changes every year, so it's impossible to say anything definitive about how it will be in the future.