Sounds like the Nintex Form control "Repeating Section" is a fit.
Controls not staying where they were placed has unfortunately been a feature of classic forms since the very first version.
If the panel isn't actually necessary then don't use it. If you need to use the panel (for show/hide etc.), never put a title on it.
In my experience...it's often necessary on complex forms to save the form twice. What I mean is, you move the controls around on the canvas...they look ok. Save. Next time you open controls have moved and are overlapping etc. But then I generally find they can be snapped correctly into place and then once saved for the second time they stay there.
Can you use the new reponsive designer for your form? That allows upto 6 controls across the page now.