How is moving homework out of the home helpful? Ah, let us count the ways!
The long academic day is mentally exhausting for most children, especially for those who have to work extra hard due to learning or attention disabilities. Over their entire school careers, they've come to see that home represents the endpoint to the school day's stressors and functions as the starting point of recovery.
What is your reaction to this picture? Do you crave this comfort? Does is make you feel cozy? Do you wish you were there? This is what home, at the end of a school day, looks like to your child. In the same way Pavlov's dogs salivated at the sound of a bell, our children make the cognitive transition from school to rest when they get home. This association has become automatic. It is strong and visceral, and will be difficult to undo.
Rather than continuing to spin your wheels by constantly nagging your child to do their homework, allow them to create a new association by finding a "homework place" outside of the home. Public libraries, coffee shops, and possibly even your child's school (many are open after school hours, just check first) are good starting places. You may have to try out a few, but ultimately, we want your child to make a new association, that wherever this place is that they settle on signals "homework" to them. With time, it will become automatic.