First, I'm sorry you're facing this situation. I will be sending lots of positive thoughts your way!
The government has many funded grants to help with either an eviction (emergency assistance to attempt to halt an eviction and assist in getting caught up on back rent) and/or assistance with affordable re-homing.
Please check out: http://www.needhelppayingbills.com/html/housing_an...
Generally, you can locate your city (search by zip or city) and there are a few options listed with phone numbers where you can call and request grants for assistance with catching up on your rent, or placement in the event of an eviction. Often times they can assist in stopping an eviction and work with your landlord to arrange payment directly to the landlord, and what the grant doesn't cover would be the responsibility of the tenant.
Don't delay, though. There can be waitlists and assistance is given in order of need. With your 2 small kiddos it sounds like your situation would be a priority!