The "Army's navy" is not heard of much, but suprisingly does a great deal of work. The Army actually has the responsibility of moving it's logistics over the shore (LOTS) and that also includes port operations. When the military takes over a port, like Basra in Iraq, the Army is responsible for running it. There are specialized Army units that are specifically designed to operate ports in a joint enviroment.
To support the LOTS requirement, the Army has a large number of smaller vessels. Virtually all of them in use today are Navy designs, and bought piggy-back on Navy procurment. The Army's LOTS requirement is basically to be able to unload a ship, and move the logistics over the shore. It is not an "amphibious assault" requirment, but simply the movement of supplies over the beach to where ground transport takes it further inland. Additionally, there is a smaller requirement to be able to move supplies up inland water ways in regions that have usable waterways and unusable roads.
The DUKW was designed when the Army had a requirement for amphibious assault. That no longer exists. One thig the DUKW's did quite well though was LOTS. They would act as small lighters and load directly from the ship off-shore, and drive right up on shore to deliver and repeat. Due to the small capacity (it was a 2.5 ton truck), it wasn't the greatest for this job, but it's abilty to do the job without other facilities made up for it.
Replacements were more purpose designed as amphibious lighters. The LARC's, etc. kinda sucked as trucks due to maintenance issues, but had a larger capacity and therefore a higher through-put speed. In the 1980's the Army bought LACV's which were hovercraft that could carry 30 tons. They were smaller than the LCACs used by the Navy to move the USMC around. The LACV's were fast and fairly capable, and could really do a good job at LOTS. The Army never had much more than 30 or so and got rid of them in the 90's. When you buy small numbers of things, cost is a killer in unit cost and replacement parts. The LACV's were neat, but other developments made them not as cost effective.
You have to remember that most of the ships up until then were older style freighters that used cranes to off-load over the side. The Military Sealift Command had gone to great lengths to improve the fleet though and now nearly all of them are Ro-ro, or roll-on-roll off, types. They have built in hatches and ramps to unload rapidly on a pier. The latest Army ship, which are TSVs, are basically modified high-speed commercial, ocean-going ferries. The two available test vessels of this design (A Navy HSV and an Army TSV) moved one helluva lot of stuff during OIF. While no one was paying much attention to it, those two vessels really moved far more equipment than any other combination and really proved the concept.
The system as it exists now is to use a portable pier to offload the ro-ro ships, which just drive the stuff directly off the ship and wherever it needs to go. Older style ships, and ships waiting on pier space can off-load the old fashion way into Army lighters, who then move the supplies to a crane that off-loads them. Since many of these lighters are actually the same landing craft the Navy uses, there is a limited capabilty to off-load directly on-shore, but onward movement becomes a pretty big problem.
In typical Army fashion, the "skipper" of any vessel is a Warrant Officer. While a Commisioned Officer commands the actual Transportation unit, the commanding officer of any large vessel enough is a Warrant Officer. We always called them "boat Warrants". Small vessels are run by NCO's just like the Navy does. Several Navy NCOs that got cut from the Navy went "blue to green" and became Warrant Officers in the Army as skippers of bigger boats. Most of the Army's watercraft fall under the Transportation Corps. By all accounts TC does a very good job managing them all and it's become a pretty interesting niche in the Army really. Few people know they exist, fewer still know any details, and they pretty much operate in their own little world away from any of the BS that plauges most Army units and many Navy ones. There doesn't seem to be any problem with the Navy, and they get 110% support from the Navy when required, but they almost always are working with them in a joint enviroment anyway, so it's pretty much a "purple" deal there.
There is no amphibious requirement for Army vehicles. They stopped swimming M113's due to cost and safety issues. The only thing amphibious would be something left over from "back in the day". The abililty to swim a vehicle adds all sorts of cost issues in design, complexity and maintenance. Due to the fact that most vehicles really suck at it, the viability of an opposed river crossing is nil. If you aren't going to cross opposed, you can pretty much build a bridge. Swimming and snorkeling aren't really what they are cracked up to be. There's very serious issues with either that make it questionable.