Exodus 1: 15-21 is always a troublesome passage with regard to anything other than complete honesty being sinful. In that passage, God obviously viewed the saving of the babies as being of a much higher priority than confessing honestly to Pharaoh. There is also I Samuel 1, where Hannah leaves a toddler (Samuel) in the care of a man whose sons are among the worst sinners of the time. Without knowing the age of your child, the situation, and other things,
I really don't have an opinion on your proposed actions except that you need to clearly count the potential cost of this before doing it.
Here are the questions I have (which echo some things others have already said):
- What are the legal ramifications for you and your friend and your child? Do you know for sure what the potential consequences are? Do a Google or Bing Search on "School Enrollment Fraud" for your state and city and find out. This may not be a trivial thing! In some places, records fraud is a felony (including jail time) and your child could be expelled.
- Is home schooling an option? Are there any private school options?
- Is this something where you and other parents could unite in some way to make a difference?
- Is it possible for you and your family to actually move to a better school district?
- Is your child at an age where schooling is mandatory? Could you wait to enroll a year and plan to move before then?
- Could you actually move in with your friend to actually live in that district/zone?
- Is your lifestyle situation such that you could be a volunteer worker or something else so as to spend time in the school?
- How much on-going lying will you and your child (and maybe your friend) have to do to maintain the facade of a different address? This isn't about filling out papers once; it's about making sure no one at the school (including teachers, peers, administration) ever finds out. What will this do to your reputation?
- What happens if your friend moves?
- Is this situation God's way of pushing you and your family to a lifestyle change of some sort (such as moving somewhere or taking a different job)?
Think long and hard and prayerfully about whether or not God is directly calling you to violate local laws, or if there is some other option He wants you to take. Consider too who else will have to assist you in violating these laws. This is not a "one and done" action; it is a decision for an on-going "out of the system" lifestyle that will have to be maintained for the school year (or longer).
Ultimately the question is, what is the path God has planned for your child? Will attending a "better" and "safer" school make them a better person than the poorer school? Will attending the poorer school give them a perspective on life that being more sheltered wouldn't? Also, "better" schools have their own sets of problems that may not be as visible, but can leave lifelong scars as well.