you can achieve this with CSS , which works on both classic and touch UI.
you need to add below CSS rules in RTE editor which load for dialog editing,
you can create your own clientlibs with cq.authoring.dialog category.
- text-align: right;
- direction: rtl;
Screenshot shows right to left editing and CSS rule.
Note : I added CSS rules just for testing, you need to specify selector which only applies for dialog editing.
If you want global change you can write below:
.coral-RichText {
- text-align: right;
- direction: rtl;

Thanks
Arun