The trick is to use enough velcro to sustain the weight of the blanket. My friend has a lovely leather sofa and love seat which her doggies have designated as their beds. She was noticing that even though they are small dogs, their claws were leaving scratch marks on the leather. She has two or three great looking throws and blankets that she stitched velcro to the entire length of one side of the blanket. She then placed the same size length of velcro on the back of the sofa. The length was the key as it easily support the throw/blanket weight and prevented the blanket from slipping.
Another good friend owns five high end furniture stores here in the San Francisco Bay Area. I quickly placed a call to his wife who is an interior design expert to see what she had to say. She mentioned velcro, but also mentioned that you can call an upholster that can insert blanket buttons on your leather sofa. What this is comprised of his attaching matching leather buttons on the back of your sofa. The blankets or throws then have the appropriate loops that are placed over the blankets. There is an initial investment, but it works well. I often noticed the way the sofas in the stores were accented with throws and decorative blankets, wondered how they were kept from slipping, never bothered to ask-- but now we both know!
She also stated that you might even be able to install the buttons yourself. She mentioned that if you go to a fabric store, you should be able to find matching buttons that once inserted into the leather, have spring clips that open underneath the leather (or other material) to keep the buttons in place. You would then purchase matching rope trim to make the loops.
Let me know if you have further questions or concerns. I will check back.
The button solution does not need to be permanent. You would have to instruct your children how to carefully unbutton the blankets from the couch. Depending on their age, this may not be easy for them to manage.
I am a Mother and also now a Grandmother. What you might do is what my daughter has done. My daughter purchased each family member their own blanket/throw to be used when watching TV. My two grandkids aged 6 and 2 also would bring out their pillows to get "comfy" while watching their favourite videos. My daughter was driven to distraction by the constant pile of blankets and pillows that were strewn across the living room. She went to Pier One and purchase a lovely decorative basket which the kids now neatly fold their blankets and place their pillows in. They know when they are finished watching a video or TV, that they must place these neatly in the basket otherwise they will not be allowed to watch TV the next time.
This may be a solution to place into play after you have placed the buttoned blanket over the couch. Your kids would then only have to take use their individual blankets over the other couch blanket.
Another friend of mine who is also a Grandma mentioned to me that her six grandkids would complain that her leather sofa in the family room was too cold to the touch in the winter and two sticky hot in the summer. She tried purchasing them their own throws, but these can be often slippery and the kids would become frustrated. She went out and purchased a relatively inexpensive pre-made slip cover that not only protected her couch from the kids, but solved the problem. When it became soiled she threw it in the washer and dryer. She would remove it when the kids were not visiting.
If I come up with any other ideas, I will certainly post them for you to review.