@Kevadu You're not missing anything big, but I do have my own thoughts about a couple of the details:
"Getting more holy trees"
Mistis is in the world all the time, Holy trees just gather it in fruit form. (Ref end of Ch 2). But the actual growth of the fruit takes magicians efforts (Ref early Ch 3). So unless you put mages into singing for them, the new trees won't give fruit. In the future if they start adding mages, that's probably because they need (and will use up) the magic, (maybe they are creating a magical internet) so for now and near future there shouldn't be a problem with more trees. (Plus, if there are more trees, there's less reason to throw magical nukes at them if there ends up being a war, since they are no longer "single point of failure"). (Ch 5 onwards imply that holy trees always gather mistis - if we want to work these to together it's probably "holy trees always gather mistis, but need to be overloaded if you want fruits anytime soon, i.e. you need to forcefully add extra magic to them for that)
"Queen dowager wants mistis back by returning summon even if nobody knows it can be done"
The possibility to get mistis back was just a "winning ticket" since it would solve her plans right away. Her second level plan was "if the foreign queen is gone, we can do as normal royalty and create alliances by marrying the king off". (Ref early Ch 4) Unstated, but she might also have had a third level plan of "If a foreign queen runs away like this, maybe I can put an end to the tradition of summoning foreign queens, that way we can start accumulating mistis in the future and at least not end up powerless in the upcoming arms race" (Note that she's fully aware of the mistis fruits usefulness as magical nukes, and nuclear arms races make people silly)
"Nobody talked to the king" - "Gred the liar" - "King finds Shize, but does nothing"
No, Gred didn't want anyone talking to the king since he might side with his mother. (Reasonable possibility, from his pow. Plus Gred is a bit stupid).
King finding Shize and doing nothing - yea, that bit would have been better written out of the story. But since it is in there, let's call it "too much respect for her will", based upon the fact that she was not in danger (didn't seem to be imprisoned) and she had made the king make her a "bug out bag" earlier (which he could read as "I might run away without you sometime") - so he's doing the "if you want to see if someone loves you, let them go and see if they return" thing.
Shize then does returns on her own to the king (with some help of her friends). (Ref mid to late Ch 4). King then talks to Shize, she explains what is going on (but no pages are wasted on it since we readers already know everything) and they even solve a misunderstanding (he convinces her that his wish is for her to remain, i.e. he's in no way interested in his mothers plans). (Ref start of Ch 5)
(Then they start worrying about it again in the end of Ch 5, that the king might have to put his country ahead of his own will, which is kind of noblesse obligee, but they didn't have any time to make a decision either way since kidnappius interruptus. Shize would probably have talked to her husband again over it though before any decisions were made)
"Kidnapping even if they could just have asked her"
At the time she was under control of bodyguards, and hunted by Gred (and by the Queen if she too has figured out Gred tricked her), plus the plan was all along to get her unwilling self to the neighboring country (or wherever Gred was born in the first place). Anyway, the decision to kidnap first and ask questions later makes sense from a "this meeting must happen" perspective. It's stupid from a "also it would be good if she comes ready and willing to negotiate" but they lucked out that she was willing to overlook it as long as she could be reunited with her family.