I hope the child was not badly injured.
Liability may have to be sorted out in a lawsuit and it sounds like it could be hotly disputed. Please be sure to put your homeowners insurance on notice immediately (they will provide you with a legal defense if a lawsuit is filed) and take pictures of the fence ASAP, save all of the correspondence you have regarding your efforts to get the owner/manager of the apartment complex to maintain the fence - or prevent damage to it. If you do not have correspondence or email, write down the dates you can recall making this request and the names of the people with whom you spoke.
This response does not constitute legal advice and does not create an attorney-client relationship. Due to the complexity and ever-changing nature of the law and to the limitations of this forum, this information may not be adequate for your specific situation.
I hope the child is not severely injured. You should consult with an attorney in CA immediately. Most states have very strict laws concerning liability for dog bites. You may be right that the apt. has not properly maintained the fence, but this was something that you appear to be aware of us well, which could be used as further support for the argument that your dogs should have been leashed if you knew they could get through the fence. If you are sued for the bite, contact an attorney immediately.
I have a case in my office similar to the one you describe, except I represent the person attacked by the dog. The insurance adjuster is arguing my client failed to maintain her side of the fence. I am arguing that the dog's owner failed to keep their dog in their own backyard.
Contact your homeowner's insurance and make a claim. Send them all of your documents. They will defend you.
You can expect to be subjected by Animal Control to abated measures which won't be excused by the fence issues. You have a duty to your neighbors to contain your dogs. Your dogS trespassed onto the neighbor's property and injured kids; I would have summarily and totally abated your dogS had I been there. Your best hope is that the fence was damaged under circumstances that you lacked both knowledge and reason to discover the damage before the child was bitten.
A roundup of the best tips and legal advice.