I'm confused as to how the twin boys affect the need for a skirt/covered trapway. For a heavily-used toilet, you want a reliable one for sure. If you prefer the lower height, and want a good value, the Toto Original Drake CST744E is a great choice.. Elongated, regular-height. It just doesn't have a skirt. Great flush. Sturdy. Stands up to use. Resists clogging. I think Terry installed a bunch of them as commercial-use (i.e. in the public restroom) toilets in his church, after he had installed one in the pastor's quarters and she got to see how well it worked, IIRC. They are regularly used in commercial settings because they clog so rarely. The "E" version is 1.28gpf, and thus is a Watersense toilet. It's a standard installation.
For a street price of about $100 more than the Drake, the least-expensive skirted Toto toilet is the dual-flush Aquia II, CST416M. This is a regular-height, skirted, dual-flush, Watersense, elongated toilet. Terry sells a lot of them to customers who just keep ordering more. Like all dual-flushes, it has a slightly-smaller water spot than a single-flush. Like most dual-flushes, it doesn't have a flush that swirls and doesn't have a siphon jet at the bottom. Instead, it uses a "washdown" flush, where all of the flush water rolls down the sides of the bowl, and you don't usually hear a gurgle at the end. But it does evacuate everything that's in the bowl, and has decent bowl wash. Like all skirted toilets, it is a little more complicated to install, but any decent plumber shouldn't have an issue.
Here's a video of the Drake flushing paper:
Here's a video of the Aquia flush by ToiletFan1 (a kid who loves toilets). The smaller flush comes in about the middle of the video, followed by the larger flush.