Very interesting idea about organizing a contest about #travelwithricheros going to Rhodes!
I have been there in 2014 for one week. To organize a whole day with all your family is not at all easy, because you are many and you have children also. I will try to give you some advice for one whole day!
After you wake up and take breakfast, if you have a rent car, go and see Lindos! It lies on the east coast of the island and it is about 50 km south of the town of Rhodes. There, you will find a fine beach, where the children with grandmother can stay while you and your wife will take a ride to Acropolis. You can use donkey to go up, but it not be so heavy to go by feet. It's a popular tourist and holiday destination. The beach is very soft and proper for children and low level of water.
After 2 hours here, you can take back the road to Rhodos, but make a stop to Villages on the coast. In first village, Charaki, you can take lunch, because here you can find the usual taverns, restaurants and bars.
After lunch, you can go to Faliraki, where you can see Anthony Quinn Bay (here was filmed Zorba The Greek movie). After this visit, for the joy of children you can go to Water Park, which have has waterslides and a wave pool and special places for children.
After couple of hours here, you can go back to hotel to take a shower and change your clothes. After the sun is down, you can go in Old City for a walk and dinner also.
In the Old City you can visit Palace of the Grand Master of the Knights. In Old Rodos you can find souvenirs and a lot of restaurants.
After you finish with eating and shopping, must go and see the port and the One of the Seven Wonders of the Ancient World, Rodos Colossus (or a part of it:)) - here you can go with children or you can leave them with your mother in law:)
I'm sure will be more that enough for you and your family this day and the next day must come back in the port and if you don't have sea sick, take a ferry boat and go to visit Marmaris (Turkey). Will be very interesting even the ride with ferry.

Hope these info will be helpful and you will adjust at your needs for a wonderful holiday!

Enjoy the trip!
Mada