So give some intermediates between Pandemic Legacy and the COIN series
Guess I'll leave them for a year or two!
Good question. I was going to make some suggestions in my original response, but realized I couldn't provide a useful response without stewing on it for a bit.
From my perspective, the objective is to find a game where the level of effort required to learn the game mechanics well enough to effectively apply those mechanics in a competitive manner is enjoyable and not burdensome/frustrating. A lot of factors impact this assessment including game complexity, how well written the rules are, how experienced the players are in general, have any of the players played that specific game before, how enjoyable the theme/subject matter is to the individual player, how cool are the bits/craftsmanship of the game itself.
I'm not really saying anything original here, but rather trying to articulate some of the factors that impact my enjoyment of playing a new game. So, since I don't know what theme/ subject area might be enjoyable to you and your daughter that factor is left out here.
Given all that and a desire for "stepping it up and I'm looking for another non-abstract challenge" while heading toward a COIN capability a couple games come to mind.
Washington's War: Card Driven Game (CDG) where there is a relatively low level of complexity and interaction within the card deck. That is, the cards mostly provide the resources for moving the pieces on the board and there are only a few "event" type cards (none of which are conditional on other cards in the deck). Also, both players draw from the same deck. The game does a very nice job of introducing the concept of a card driven game mechanics coupled with a set of point-to-point game board mechanics. Plus it teaches a little American War of Independence history along the way.
Twilight Struggle: The next step in a CGD in that the deck complexity is increased by a noticeable level. While both players still draw from a shared deck, there are cards within the deck specific to both players. So, there is an increased emphasis on deck management in that one must learn to exploit cards beneficial to them while mitigating the damage from the enemy cards. Also, the "card angst" is increased because each card consists of both an event and a value that is used to drive each players board position. Typically, the higher the value of the card the more powerful the event. Finally, the deck is broken into three phases, Early, Mid, and Late with some small amount of interaction between the phases. Also, the later the phase, the more one needs to be concerned about their board position in Africa and South/Central America beyond the initial struggles in Europe, Asia, and the Middle East. The game does a nice job of providing a historical context for the Cold War.
1989: Dawn of Freedom: The sister game to Twilight Struggle (TS) that has a bit more complexity to it, but covers the Cold War period leading up to the fall of the Berlin Wall in a little more detail than TS.
COIN Series of Games: CDGs designed for up to four players, but with mechanics for playing one, two, and three player options. The additional step in complexity for this series of games doesn't originate from the nature of the card deck, but rather comes from the game mechanic of deciding to what degree a player should utilize each card in order to best enable the conduct of a series of highly interactive actions. Also, one player's choice directly impacts another players' choice of actions, plus the turn order itself has some amount of uncertainty based on card designated turn order and choice of action. Typically, on their turn each player has a choice between playing the event on the card or conducting one or more of a set of semi-unique actions associated with their side. This is compounded by whether to play a limited set of choices (which then limits the next player's options) or an expanded set of actions (which also allows the next player to increase their options). This is all compounded by a set of Victory Conditions that are asymmetric to the opposing players. So, while the cards themselves are mostly no more complex than most moderately complex CGDs, the surrounding game mechanics is where the complexity and challenge comes into this series of games. Initially, one should plan on just pretty much going with the flow in these games in order to find an effective set of strategies for each side. These games do a pretty good job exposing one to various aspects of military and political history.
Although I haven't played them yet, it is my understanding that
Wilderness War and
Hannibal: Rome vs Carthage are also highly accessible games in the complexity vain of
Washington's War.
All of the above are great games in their own right and should serve as nice steps along the way to playing any of the COIN series of games.
If you are after general strategy type games that up the complexity from Pandemic but aren't card driven please just let me know.
Bill
P.S. I've also enjoyed playing
Sword of Rome but only in a four or five player mode, so I can't speak to how well (if at all) it plays as a two-player game.