grandma wants the names on the front, or she will just turn it over to study them and use it backwards...regardless...
the best way to get as many names as possible at one time is to do it at the party... then you will only have to deal with the people who couldn't get there. This way, lots of moms and dads will just sign their kids names for them when they couldn't make it... fewer strays this way, and a way to include those loved ones who have passed away... and someone will have to put grandma and her husband in a square...in the middle, maybe?
Next, take squares of muslin marked with a border so they will write INSIDE the square... iron them to freezer paper so people can write on them easily. buy three or four fabric pens in dark brown or navy blue. (you don't want to run out of ink in the middle of this project. both colors read as black when on light fabrics, but will not have the stark look of black. they will be softer and blend better with the colors on your block pieces. Now use the section with the name to cut as the center or side piece in whatever block you like. Even a simple log cabin would work... one side of the logs in your 'family code' color and the other side in a neutral. Everything goes with navy or chocolate. All the other family colors would tie together beautifully with each block having something in common. your family color idea is great...can you find 12 separate colors that aren't just shades? ask everyone for $.50 or a $1 donation (not mandatory) to help cover the cost of batting and backing... i think you need to really consider using one block with all the colors. it could get really busy with 12 different design blocks.... but whatever you decide on will be lovely and she will love it... just set yourself a deadline...like 3 months from the party and then send the picture of the quilt to all family members who give you an email address... this needs to be done at the party, too. good luck and half fun...