For two people and four legged son. ( woofie)
Thats very endearing the way you put it. You have to call around and ask if they accept 4-legged children. It may be cheaper to rent a room in someone's house who wont mind pets instead of a hotel. I just dont know what motels accept them.
Figure at least $1000 per month on long term rental agreement May be difficult to find one that accepts pets. Good Luck
Nobody here can answer that, You have to look up hotels in that area, find out which ones allow pets & long term stays and find out their rates. Nobody is going to do your research for you.