The shaking and panting are just symptoms that she is scared, under stress or in pain. If she is experiencing separation anxiety, then she should be displaying the same behavior when you leave her for any reason. So if she only displays this behavior when she is separated from the cat, Keep the cat and her in the other room. There is also no reason why the cat can not be crated as well right next to the dog if that help with her anxiety
There are some things that help with separation anxiety such as DAP collars. They use a pheromone similar to the one a mother uses to calm he nursing pups and is quite effective in cases like this. It can also be used with medications as well. Medications can be helpful as well. Read about these here:
You might try desensitization training as well. Practice putting him in the crate, going in the bedroom, opening the door immediately and rewarding him with a hot dog treat if he did not react. This teaches him that you leave but come back quickly. Once he seems to not do anything when you initially leave, lengthen the time he must be quet for you to come back in. Change the time as well. Make it 2 minutes one time and 10 mintues another, so he never knows if you are gone for an hour or gone for 2 minutes. It helps him stay calm for longer periods of time, just be sure you reward him when he is good.
Now dogs can also tremble as the result of seizures which can happen with low blood sugar levels. So if you think this might be a contributing factor, you might try a drop of pancake syrup or karo syrup on her tongue or a small meal right before bed. That should help if low blood sugar levels are contributing to the issue. Anxiety can also cause some excel bile issues which might cause trembling and panting as well. The small meal should help with that as well.
Try some of these suggestions and let me know how it turns out. Remember that dogs will exhibit behavior that gets them what they want. They are opportunistic so do your best to ignore the bad behavior. Ear plugs can work wonders.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer.