I think that all of the situations are indeed different and offer their own complications. The landlord could have had a family member with a situation that required the money as soon as possible. You never know.. they also could just be a jerk and want to sell it and not give you much time. A month is better than a week though.
Moving places is definitely difficult though, and it’s not something we want to undergo often that’s for sure, particularly with kids! I hope you can find a suitable place soon and have the moving process go smoothly!