Designers, Typography Experts and people who like cursive writing, is this example "correct"?

The sample looks like a style of calligraphy to me. If you are interested in calligraphy, I’d suspect that you’ll learn more in one class than you could from reading about it. And maybe I’m not understanding your questions, so please ignore me if I’m off track.

Are you trying to write longhand or set type?

No, the spacing isn’t right, and the I of “in” ought to be lowercase, not small cap.

I think you would really enjoy Elements of Typographic Style, which is lovely, and also (perhaps a bit off-topic, but relevant if you are thoughtful about the form of written words) Bringhurst’s book The Solid Form of Language. I’ve linked the Canadian listing for the latter, because the US version is ridiculously overpriced. This book is a beautifully made thing.

You are talking about calligraphic ligatures.

@Jeruba – Trying to set type. I can definitely change the “i” in “in”. How’s that for a tongue twister. Lol When you say the spacing is wrong: is it too much space between the “Rest” and “Peace.” Also, is the “P” in peace laying to much on the “n.” This isn’t a vital piece of art, btw. As some of you know, my dear neighbor died. I’m just trying to make a nice piece of art and this totally tripped me up.
@glacial – I’ll definitely check that book out. Thanks!

Are you designing your own typeface or working with existing?

The space before the e is too great in “Rest” and too small in “Peace.”

What are you using this for?—sign, card, program? My sense is that a less ornate, flourishy font might be a much better choice for conveying the sentiment of peace. This looks agitated to the point of distraction.

A friend of mine is quite successful with this; you may enjoy his blog: seanwes.com