The only problem with side-lying for an epidural patient is that the epidural tends to become stronger on the dependent side and wear off on the upper side. The people in my experience who have the most pain in labor are not folks without medication, but folks with a poorly working epidural. I think maybe because they are so expecting relief, that it's even more discouraging to have pain after an epidural is placed.
Depending on how numb mom is with the epidural, upright position can be used. We use hands and knees still a lot. We usually have mom kneel on the bed and rest her arms over the top of the bed with the bed up almost in a chair position. We also have had many moms squat with the epidural if they have at least a little movement. I'm not crazy about squat bars, though. What I do is lower the feet all way and have mom sit up at the edge of the bed (this is the type of bed that breaks down for delivery.) Then when a contraction starts, we help mom lean forward and squat on the foot of the bed, then help her back to sit on the edge between. This works great if there is a nice strong dh type around, and a helpful doula type, too. Otherwise I wear the nurses out (which at least in my hospital they are willing to help holding someone in a squat, but you might not find such nice nurses elsewhere.)
You have to be careful to hold onto the mom with an epidural, especially if she is pretty numb. Also, you can turn the epidural off for pushing, usually, and then turn it back on if you have to proceed to operative delivery of some type.
Pushing is much easier if you can move freely, though, so avoiding the epidural altogether makes it easier.
Some anesthesiologists also prescribe bedrest for all epidural patients and will not allow any other positions, so you might want to check that out in advance.