@laura.brunnen indoors is harder because the bike is static on the trainer. The key is a strong core, and engaged glutes and hamstrings, so that you can support yourself without putting too much weight on the handlebars. By using your glutes, hip flexors and hamstrings, you are able to pull up on the pedals just as much as you push down. The feeling you have of mashing your knees is probably because you are not pulling up - and only pushing down. It takes practice, practice, and some more practice. It took me years to get to where I am, by practicing every week!!
@paulamunt I have a Tacx Neo and yes, it does have some side to side movement, which is very helpful. Others use a rocker plate, like @goldendogy.
Here is a video of how this technique translates out on the road: