What is the ruling on combining and shortening prayers while traveling for 12 days, distributed between a hotel and the family home in Abu Dhabi? Is it permissible to combine prayers throughout this entire period?

If the country where your family and husband reside is your native land, then your journey ends as soon as you enter it, and consequently, you are not permitted to shorten or combine prayers. Similarly, if a traveler intends to stay for four days or more in a country, their journey ends, and they are no longer permitted to shorten or combine prayers.