My expert diagnosis (😂) of Kate's abdominal problem was peritonitis. The story fits and the recovery time's about right, assuming the infection had spread and they had to cut. She may well have been on heavy antibiotics or steroids when the puffy-face car picture was taken.
Another common but serious event would be ovarian torsion, also requiring laparotomy and a fairly long recovery. Could've been something like a hysterectomy, of course. I can imagine the RF being reluctant to share details about the future queen's reproductive organs, rightly or wrongly.
My similarly expert relationship diagnosis is Trouble In Paradise, but it's probably just a rough patch and things will seem back on track by the summer.
And those apps that make a composite from your best shots of the same scene never work perfectly!