I am soooooooooooo sorry to hear about your little one's poor wee foot!
I do not have any experience with the $$$$ part of it but don't think you will need to take out a mortgage..........I'd use a credit card and then if it comes down to it.......get the second mortgage to pay off the credit card.
I always get a zero balance on one of my credit cards just for such emergencies with my babies!!!!
Hope all works out and the foot is okay with vet care!