$2,000 · Wanted-home for rent

Desperately seeking a home to rent asap. My 3 year lease is up and I’m running out of time. I have applied for many houses but with how the demand is right now, even with my great references no one has chose me and my family. I am a single mom of 3 and have 2 very well behaved medium sized dogs. I know it’s hard to rent with pets but I have a special needs son that would be very upset if I had to re home them. They calm him down on bad days and when a child has autism a change like that is not good. I love my family and I’m a very hard worker. I just need to find a very long term home. I have great references.