how would you suggest keeping her at a walk?
Yup, agree with Saddlebag. You simply block her forward movement. Similar to how you would ask her to stop BUT you aren't going to give her that full
cue because you simply want her to slow down; not stop.
She's seems to think I want her to go fast in the round pen (whether loose or on the line). I can lunge her in the arena on a line and get just a nice slow walk or easy trot no problem. But in the rp, she really moves. Nothing out of control, just no walk. Also, what's the typical way to ask for "whoa" WITHOUT a line?
Myself personally, I like to keep a horse on the line until we both understand each other well. Free lunging is fun, but I would suggest keeping her on the line right now until you get a better feel for each other. The line just gives you an extra point of control, if you need it.
When I ask a horse to do things in the round pen, my cues are the exact same
whether they have a line or not.
So to stop, I use my body language to stop their forward motion and use the word WHOA. I never actually step in front of the horse (that's a dangerous move!) but I will turn my shoulders/chest to face them, and I may raise my arm to "block" them. If I need to reinforce the stop with the lunge line, I will, but I usually just pretend it isn't even there, which makes the transition to free lunging easy.
This is my own personal preferance, but when I ask a horse to WHOA, that's what I want them to do = stop. I do not want them to turn toward me. I do not want them to walk to the middle of the circle. To me, that is not what WHOA means. It means stop moving your feet, now.
I teach them that's what WHOA means so that when we translate it to the saddle, it means the same thing (stop moving your feet).