I'm relatively new to playing Caldara decks, but this is my take on the archetype, and it does not disappoint! I have _crushed _quests with this thing - The City of Corsairs on first try, and several nightmare decks as well, for example.
There are several possible opening hand combos you could be looking for. Prince Imrahil would be decent, but you probably want to see an Imladris Stargazer and Zigil Miner. If it's a quest that requires early heavy questing, you might also want a Pelargir Shipwright, as the inclusion of Beregond means that you're actually starting with below average willpower. I've found that things usually work out, however, and I prefer Beregond's defensive prowess in a deck that otherwise lacks a powerful and reliable defender. Once you get Blood of Númenor on him and can stack up the resources with your miner, you'll be in great shape, especially if you also get out your Unexpected Courages. Desperate Defense is there as more of an early game defensive option before you get Beregond fully set up.
Arwen Undómiel allows you to get expensive allies into your discard pile and to get resources. She allows you, for example, to be able to play a Prince Imrahil, Sword-thain, or a combination of Imladris Stargazer and Zigil Miner in a single turn, which can be a huge help to your startup.
The biggest struggles this deck faces can be early game questing (though you'll usually be okay in the end), a small number of unique allies to target Sword-thain (though I've found this build to generally be pretty good - I don't want to be sitting on a hand or discard pile full of unique allies in a deck with poor card draw, especially when the non-unique ones are most of the point of the deck), and lack of card draw. The discard pile shenanigans are kind of a form of pseudo-card-draw, as is the effect of Imladris Stargazer. Elven-light can help out once you get it, but it's hard to give up that resource when you want to keep paying for Fortune or Fate again and again. If you're playing solo and run into issues with card draw, you could consider some Ancient Mathom to assist. Finally, if you have 3 core sets, this deck would probably benefit from a third of each Unexpected Courage, Dwarven Tomb, and Fortune or Fate.
If you struggle with early game questing, why not swap out Beregond for Cirdan? Also, maybe you should put in some Ally Glorfindels.