I'll try to answer some of your questions! We are also doing LHFHG with my 6 and 4yo boys (the 4yo--loosely!). My oldest is doing Preparing.
Personally, I let the kids write in the workbooks. I think it's probably just as cheap or cheaper to buy new ones for the next kids that come along than it is use up ink and paper. And I don't like a bunch of loose papers because I'm not so great in the organization department.
So I try to avoid that as much as possible.
When it comes to hovering and discouraging, I can tell you that this was something I really had trouble with when I first started homeschooling. Now that I have a few years under my belt and can see how things progress as they get older, I have a better perspective and lower expectations for my youngers. I'm assuming from what you wrote that your oldest is the one using LHFHG so she is probably just learning to read and write and is young elem age? It's SO EASY to get carried away at first and expect things to happen faster--for me, handwriting just about did me in. I'm embarrassed to say, many tears were shed over handwriting worksheets in the first year.
Everyone told me to relax, that she was still young, and I didn't even really NEED to be pushing for perfection right then, but I didn't believe them.
Now that I have my next child learning to write, I know that those imperfect t's and a's will someday straighten themselves out as my ds develops motor skills and has more practice.
In terms of leading to the right answer vs. correcting mistakes after the fact, it is a fine line. It has been a learning curve for me to figure out the right balance. I don't feel bad modeling the correct way to do something many times before I expect my kids to figure it out on their own. I guess it also has to do with the subject, also. Your dd is at the age where formal grades would not be kept in any school, so you don't have to worry so much about keeping grades yet. There are years and years and years and years ahead of you where your dd will have practice finding the answers on her own. At this age, I let mine copy my example, or I lead them along how to find the right answer (as in comprehension questions). If you follow the guide, the questions are right there for you, so you don't have to figure out what to ask!
I'm in TX, and the laws are very lax here, too. I have saved some things, more for them to see how far they've come or to have an example of their early work than anything else. I use my guide with checkmarks as my record of what we did. I doubt anyone will ever ask.
I hope that helps some! Keep asking questions!! I am indebted to my online homeschool friends for helping me through many, many challenges.
) Do most of you let the kids write directly in the book or do you photocopy the pages for like math and "do it carefully" activities? I have 3 kids and wanted to use the programs again. I just didnt know what others were doing. Secondly, how exactly do you watch over their progress w/o hovering and discouraging. I want to give dd the ability to make her own mistakes while I go back to help her correct them but found I was helping her through her first day, Leading her to the correct answer. Is that wrong? Just where is that fine line? Do you save thier daily work and file it away for documentation of progress? I live in OK where the Homeschool laws are extremely lax. I will probably have a million more questions but that is it so far 
My kids all like to have their own special workbook- & it seems just as cost effective, so I get new workbooks (such as handwriting, math, Rod & Staff books) for each of them. The things that don't get written in- we all share. 