Looking for pet friendly accommodation

Hiya,
I am a 35-year-old English teacher (female) who is in desperate need of a place to stay for a while. I am looking for a double room in a quiet house, with a garden, if possible. As I am a teacher to students over the age of 18, I have not uploaded any photos but they are available on request.
My partner and I have decided to split up unexpectedly, leaving me with finding a place for me, my well-trained 10-year-old dog and 3-year old-son. Will only need a double room for long enough to save for a deposit and hopefully find a suitable place within my budget.
I'm open to living within anybody willing to take us in. My son is a bit wary of strangers at first but he warms up quickly. He also will likely only be there part-time as he will spend every other day with his father.
My sweet dog is lovely and loves everyone. He might bark if someone passes the front door but other than that, he likes to sleep, eat and play. And he loves new people. So he's less of a nuisance than the child, in all honesty.