Jib71 has offered some very good advice about the taxis.
Here is a photo of me at Komagome station and, as you can see, the rudimentary wheelchair is definitely on the small side
http://bp3.blogger.com/_n1sjt7SfiAw/...escalator3.jpg
This was too big for most taxis, even without luggage, we found a couple who would place it on the front passenger seat but this wouldn't be possible with four of you travelling together.
Rather than going for the top, expensive range of hotels and going for easy (or easier) public transport options, perhaps it would be best to go somewhere more modest and relying on arranged taxis to get around.
What really struck me at the Sheraton Miyako on my lat visit was how many guests in wheelchairs were staying there. We were upgraded to one of the larger standard rooms and this seemed ideal for a family, the downside was the bathroom which would not be easy to use. As the sofa bed option can't be found anymore (may be worth asking though) connecting rooms might be an option. Whether the accessible rooms connect to another, i don't know.
The surrounding areas are accessible, much more so than an area like Roppongi, and the optional pedestrian bridges all have elevators. It's quiet, residential, play parks nearby, and the Yamanote line is a cheap taxi ride away - there's a complimentary shuttle, but I don't know how accessible it is, I was able to walk a little bit which helped with lots of potential hurdles. The surrounding Japanese gardens are lovely, hopefully your kids will enjoy the, but do take mosquito repellant, I was here one October and was savaged, but mozzies LOVE me, much more than is usual.
When comparing this hotel to most on those depressing 'accessible hotels' lists, the Sheraton Miyako seems more appealing than I'd thought. The downside is the distance to Meguro JR station, but this is surmountable. Tokyo has a lot to offer kids, spending less on the accommodation means more money for the kind of experiences they will really enjoy (I doubt they get enthusiastic about a high thread count in Egyptian cotton sheets and upscale toiletries)
Do also enquire about accessible rooms at the Sakura Prince, Takanawa and New Takanawa Prince hotels and factor in a short taxi trip to and from Shinagawa station. All hotels are close together and are in gorgeous grounds you can partly and your kids fully enjoy which will make a lovely respite in the summer. IMO these hotels have proven to offer time and time again good value for money, not quite as swanky as a Hyatt or the Strings but the law of diminishing returns starts to set in after the upgrade from a dreary business hotel to a Premium room at the New Takanawa... you need to start spending serious money to get anything better, and then you get other problems like the way the carpets at the ANA Tokyo IC twist your wheels towards the left as you try to urge your wheelchair onwards through the corridors.