Hi swilson and welcome to the forum.
The following is based on QCAD 2 and QCAD 3 RC5 professional , however I would think that the procedure would be similar in the community edition
As you say by selecting the spline will highlight the 'control points' (little blue dots) - simply select the control point and 'drag' it to where you want to it, by using the 'snap' options you can to some extent - control this, but this method is very manual and not that precise!
You can select the 'nodes' by first selecting your spline and then go to Modify > Explode. However you will find that you will then have individual segments of the spline and as such will not be able to achieve your goal very easily here.
A better option - if you have a reference to work to or the original shape would be to use the following methods in the 'snap shots'.I used the Snap tool options to control the spline - particularly the Snap on Entity option, just use this option and click and trace around your reference/original shape.
* If it helps you can always attach a snap shot of what you are trying to achieve.
See here for the 'Free' download and trial for QCAD 3:http://www.qcad.org/en/qcad-downloads-trial