Iron-on interfacing is a really thin fibrous type fabric that when you apply heat to it sticks like glue. Because it has absolutely no stretch, once it's ironed onto something else it stabilises it and stops it moving in any direction.
That would be my first suggestion, only because I have a tonne of the stuff at home and have used it extensively for a t-shirt quilt. It makes a big difference.
If the fabric is moving a lot, that would be your best bet.
Someone else who has worked with different types of fabric might have other suggestions. Can you post a photo of what you have done so far?