Is there another way to say "We are working on to update our resort."? I do not want to use working on.
I would think any kind of phrase implying current updating, improvements, modernization, would be interpreted by travelers as "under construction", much like "cozy starter home" usually means cramped, 1-bath converted garage or other too-small structure. :-)
If you want to avoid the implication of being "under construction", you can use a more ambiguous phrase such as:
"We're always striving to make our resort comfortable and modern!"
"Exciting new changes welcome you each time you visit our resort!"
Use "We are updating our resort." (Or "modernizing" or "greatly improving")
Rarely are people interested that you "are working" (even very hard) to do something. I suspect that was what bothered you about your phrase.
A common similar problem is seen in much advertising writing that says things like, "We strive to meet your needs."
You either meet needs or you don't. "Striving" implies you have a hard time doing it.
"Working on" is surely implied by "updating", unless you are updating the resort without doing any work.
"We are updating our resort" is direct and meaningful.