Cursive is much harder to master that print
Actually, that's not true! :)
Many countries still introduce cursive *before* printing, and that's what used to be true here as well. There's lots of info out there about the reasons why printing became the 'first' script kids learn -- but it's not because it's actually easier.
In fact, cursive is easier to master for young kids. Printing - especially the "ball and stick" style commonly taught - requires picking up the pencil over and over, it's a very choppy thing. Cursive is one motion with the pencil, you don't have to reset and find the right spot 3 times per letter. Cursive also practically eliminates spacing problems, because letters within words are connected. Common letter reversals are also much rarer, because the construcion of the letter is different. In 'ball and stick', b and d are identical... write a ball, write a stick, just put one on the other side. In cursive though, d starts with the c-loop, and b starts with the l-loop. Totally different.
I'm doing cursive first with my daughter. As it turns out she spontaneously learned printed letters by herself, just from looking at books and videos etc. But when we "do" writing practice, she's perfectly capable of forming the cursive letters on her own, and can do a whole word when tracing. She's 4.
If you do decide to stick with just improving the manuscript printing for now, though, then may I suggest going for something like Penny Gardner's Italics Handwriting course, or d'Nealian print style? Unlike ball-and-stick, the letters are formed by single strokes, like cursive. The switch to cursive in these styles is actually just adding the connectors - nothing really changes about the formation of the letters themselves.
Also, I completely agree about letting it go in her journal. And that capitalization is a grammar issue (and commonly mixed up well beyond this age, no worries), not a handwriting issue as much. If she resists working on it separately, don't stress about it for now. Relax and let her enjoy writing on her own until she wants to improve it. But I would still try a few things, to see if she'll resist or not. ;) I'd suggest doing some copywork, like in Charlotte Mason style. Penny Gardner's book has lots of info and samples and tips for copywork. Lots of other great resources for copywork out there as well. :)