You're in a truly unfortunate situation. I had the same issue, got a NOIR on an H1 that had been approved 3 years back, and I already had approved I140. Few things to keep in mind -
1. You have only until July 12th. USCIS does not give you even a single day after July 12th - they can (and will) disregard any evidence you submit after July 12. So hurry up.
2. They can potentially revoke your H1B from April 2013, which means that you will be out of status from April 2013 to current. Since you will be considered out of status for more than 180 days (read up on this on the internet), your green card will not be approved.
3. Since you will be considered out of status for >180 days, they will revoke any subsequent H1B applications - meaning changing employers, going to india etc. will not help also. And, they can potentially ban you from entering the US for 3 years or something like that.
4. I said "potentially", meaning, they can decide not to revoke it from April 2013 and instead do it from June 2014, when the NOIR was issued. That is a better scenario, because then you can then change employers, BUT, it's a pretty big chance and I don't think you should let them revoke it and take that chance.
5. If all this bad stuff happens, they're probably gonna take 2-3 months to revoke your H1B. That should give you sufficient time to dispose of assets. And please, do not advise anyone to buy a house on H1B, you might as well shoot yourself.
Things you can do -
1. GET A GOOD LAWYER - do not go with just any lawyer who does not have experience dealing with NOIRs. Do some research and find a good one (Murthy is good) - be prepared to shell out money.
2. No need to say that you were working from home due to kid etc. - that has no bearing on the case. You can show that you were only temporarily working from home - you can say that it was only an exceptional day that you were working from home. Submit evidence to back that claim (any travel records, letter from client company. lawyer can advise more on this) Again, you only need to show that you were working in the office in April 2013. If things changed after that (e.g. in 2014), that has no bearing.
Your NOIR is still better compared to others - you just need to prove that your work location was indeed the client site and you were at home as an exception only.
All the best, hope you learn from this experience and come out successful.