Yeah, I agree that usability is very important. You don't want playing Dominion to feel like work.
I think the key here would be to make the tool require as few clicks as possible to use. Clicks = work. Also, because there are so many complicated interactions in dominion, we may need to track a lot of different types of information depending on the kingdom cards present, and it would be annoying for both the designer and the user if the functionality changed constantly. Obviously, if we track every card that exists in each person's deck, then we have all the information that we need (ignoring VP tokens, which can be handled separately).
The easiest way to minimize clicks and maximize information would be to have a table: each player gets a column, and each card in the kingdom gets a row. Note that this means at least 17 rows: at least 10 kingdom cards, the standard treasures, the standard VP cards, and curses. (Certain cases, like young witch, potion, or tournament, would add rows.) In each cell of the table, in nice big bold font, is the quantity of card X in player Y's deck. Next to the number are two buttons, "+" and "-".
The layout described would look a bit scary at first blush, but the use case is very simple: I buy a card, that's a single click. I trash a card, that's one click. I remodel a card, two clicks. I play a witch in a 4 player game, that's 3 clicks. (Three is already a high number -- for crazy attacks like mountebank, perhaps we consider having a dedicated button.) At the top of each column, we can compute the total VP in the deck at the moment, which I think is the information that we're really after. It would also be handy to have a turn counter, which is as simple as a single button with a number next to it.
Obviously, some minimal setup would be required: you'd have to enter the number of people playing, and the cards you're using. (Obviously, if you use the card picker on the site, then the information would be fed directly to the card tracker.) I don't think the tool would do any checking for you, because "are you sure" buttons just add clicks (work) and complexity. For people who want to use a tracker, I think the design described here would be the fastest way to accomplish the task with minimal complexity.