Yes, that is odd. Especially about your dog, it's not a matter you'd expect he would want to leave to the Ls.
I have no idea what could be going on with the lack of replies, I'm a communicator so not my style to go dark!
I would probably send an e-mail to ask about the dog again - because that is a real concern. Maybe a solution could be to establish a relationship with a housesitter now to get to know the dog, someone who can stay at your house when you're gone?
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17