First of all, I am so very sorry for the loss of your precious little Lucy - losing a furbaby really rips a hole in your heart. It sounds like you are really loaded down with your broken arm and sick hubby. Sending healing
and
in your way.
I don't have any ideas about Jake's black poos. I agree with Matese and Nanajoy - dropping off a fresh poop sample would be a good idea and a less stressful option for you and your family. If your vet feels like he/she needs to see Jake, then you can arrange to take him in.