I'd recommend Many Glacier campground for it's easy access to toilet and shower facilities. It's more bustling than some of the other campgrounds, but I do believe the rangers try to enforce a "quiet" policy at night.
The MG campground also has immediate and easy access to several great trails that would be easy for you and your family, including the valley portion of the Swiftcurrent Pass trail that passes by a chain of wonderful lakes with mountains on three sides, plus a very nice waterfall (Red Rock Falls). The trailhead is at the end of the Swiftcurrent Motor Inn parking lot which is adjacent to the campground. Just go as far as you want before turning around and heading back. Stop at Fishercap Lake about a quarter-mile down the trail to look for moose. There's also the Grinnell Lake trail (not to be confused with the Grinnell Glacier trail), which includes, if you want to do it, boat rides on Swiftcurrent and Josephine Lakes. Those would be fun for the kids. Or you can skip the boats and hike to Grinnell Lake directly from the campground.
The Iceberg Lake and Grinnell Glacier trails are also right there in Many Glacier and offer fantastic hiking, but both are a bit more challenging than the Swiftcurrent Valley (Pass) and Grinnell Lake hikes. Iceberg is 9 miles round trip and climbs 1,200 feet while Grinnell Glacier is 11 miles round trip and climbs 1,600 feet. However, you can choose to go as far as you feel able before turning around if you think you can't do the entire hike. There's a waterfall about halfway up the Grinnell Glacier trail that pours directly onto the trail itself and includes a rocky staircase that can be slippery. You'll get wet (not soaked), and I'd use a lot of caution if I was carrying a toddler.
Another short hike in the Many Glacier area is Apikuni Falls, which is accessed from the Many Glacier Road a short driving distance from the campground. It's only a mile or so in length but it climbs a steep 800 feet to the falls. Worthwhile if your crew is up to the climb.
There's a vehicle-length limit of 21 feet on the Going-to-the-Sun Road, which includes your trailer. Keep that in mind if you want to drive on the road, which shouldn't be missed.
The Highline Trail is a great choice in that it provides sweeping views and you can go as far as you like before turning around and heading back to the visitor center at Logan Pass. Keep in mind that the first portion of the trail includes an exposed cliff. There's a handrail of sorts, but you'll want to keep an eye on the kids in that area.
The best time to snag a spot in the MG campground is in the morning as it tends to fill up rather quickly (11:00 a.m yesterday according to the website). The day of the week doesn't matter during the season. Each day is as busy as the next.
Check the FAQs at the link below for more information on hiking, camping, and other info.
http://glacier.nationalparkschat.com/ph ... ?f=1&t=580