Honestly, I'd probably keep the basic status quo as it currently stands. Carol's in charge of Alpha Flight, earth's first line of defense against alien threats. That's a solid role and niche for Carol to fill that she can own; no one else is really doing that. It just needs to be handled better.
I'd bring back the earthly, civilian supporting cast and have Carol spend more time on the ground between missions and meetings. Characters like Kit need to be in her life; both Carol and the book are better for those connections. And Jessica Drew would absolutely be a main member of the supporting cast. I'd also like to re-establish some of her friendships with other heroes like Peter Parker and Steve Rogers.
I'd probably return to the idea of Carol having a base in the statue of liberty; her own secret little Fortress of Solitude hidden in plain sight. No one expects to find a hero's hidden lair in a place full of tourists!
Stories would roll between dealing with problems on earth (Skrull spies, old foes like Traveler, etc) and problems within our solar system (the Brood, Kree shenanigans, Magneto asteroid bases, etc) and occasionally (once every 18 months or so?) have Carol travel on diplomatic missions to other worlds.
Kamala and the other Marvels would play a larger role. Every major, A-list hero has at least a few legacies, sidekicks, and/or junior partners. Phylla is at the top of my list for returning Marvels, but I'd want to bring in Genis and Monica too.
I'd go for the same kind of tone as KSD's first run, or Mark Waid's Captain America and Daredevil runs; quick paced stories with a light, easy tone. Not comedies, but still fun. Not dramas, but still dramatic. Big ideas, big explosions, big heart.
I think, by and large, Carol's got a good spot in the MU right now. She just needs it to be better balanced and written better. It's not the concepts that are the issue, it's the execution of those ideas.
.....and I'd probably have her grow her hair out again. She used to have the best hair this side of Jessica Drew and I miss it.