You might want to check into Greene County to see what parks there have long-term rentals. Coeymans is at the southern end of Albany County & just across the county line into Greene county, you should be able to find a lot of campgrounds with RV hookups. I know Brookside Campground has them; and I don't think they are that far from Coeymans....although what is "near" for some is still a hike for others.
Here is something you didn't ask about, but I feel compelled to mention...
... I had lunch the other day in Coeyman's Landing at a little spot called Yanni's II. It was right on the water & the voyage of Henry Hudson was being celebrated. Great views and a fun way to spend a few hours. I am guessing there must be a Yanni's somewhere else in order for this one to be the "II"...?? Just something you might like as you explore your new area!
Sorry, I don't know enough about the area's day care or preschools.