Your baby had an experience with constipation and doesn't want it to happen again. The behavior she is demonstrating (when it looks like she is trying to push) may be trying to achieve exactly the opposite--young children can try to hold in the poop when they feel the urge to go because it hurts. It usually occurs in toddlers, but the shaking movements are pretty classic for what I like to call "The Poopie Dance". If she holds it in, it will certainly become more painful when it eventually comes out because more water is absorbed from the poop, making it harder to pass. So it is a vicious cycle.
Your job is to really crank up the fiber and water in her diet... which may mean much more than drinking some juice here and there. Offer her high fiber foods like prunes, berries, oatmeal, whole grains, spinach, and beans. Offer her water, pear juice, and prune juice at meals. If you need more fiber, you can even sneak in a fiber supplement like Benefiber--a tablespoon or two a day may really help. The goal is to make her poop soft and frequent enough so she can no longer hold it in, nor have the desire to. It can take a while to get over this hurdle, so be patient. If things are not improving in a week or two of this plan, you may need to add a mild laxative (I usually recommend Miralax, but ask your doctor) to get things back on track. I don't think your child needs an x-ray or further medical evaluation at this point, but if things do not improve you should check in with your baby's doctor.
All content here, including advice from doctors and other heatlth professionals, should be considered as opinion only. Always seek the direct advice of your own doctor in connection with any questions or issues you may have regarding your own health or the health of others.