So when they explained how they negotiated and I asked if they would extend a more realistic offer, their response was that they won't extend any offers that are more than 20% off the list price.  

Since the seller decided to sell the property he has decided to not extend long term leases.

Both parents have some upcoming work obligations that will require them to be away from home for an extended period of time, so what they want to do is have the wife's parents stay in our rental house for a while to take care of their kids (get the kids to school, go to dr appointments, etc.).

Here is my philosophy: Don't gamble if you can not afford to lose.If my project does not get extend, if my working visa can't be renew to stay in the country, well give the bank the property which I already have some equity in it (buy it right thanks to my agent who helped me to negotiate it price down) & absolutely I don't die to see the down payment & closing cost down the drain.Building wealth automatically and getting paid to do it.

Today I have started the process over again with another lender and extended my contingencies.Everyone I have talked to says that I got a bad appraisal the first time around.  

If they wish I would agree to offer them the option to extend to up to 4 months.

There are things you can do to extend that time. 

We extended our kitchen into the garage and we added about 250 sq ft to the property.

At the very least, extend the runs for each circuit back to the basement from the mudroom.  

We also have the number of Tenants all named in our leases so if someone moves in the extended family we would know how many cars are present.