I've been dealing with a friends elderly dog who pees and poops in the house. I've also helped her move to assisted living from senior housing.
About the dog. You cannot teach an old dog new tricks. The vet tested this dog for urinary infection and he didn't have one. She said since he pees in random places he's likely to remain incontinent. My brother took the dog for a while but couldn't keep him. I had the dog for several weeks. So.....my friend took him back to see if she'd be able to manage him. Her new apartment has never had a dog in it which helps.She takes him out several times/day and so far it's working. She got help from a trainer.
Sounds like taking him out or leaving him out most of the day isn't possible. Sounds like he's only been trained to use a pee pad. I would go back to using that. Why would that be too difficult? Use several scattered where he'll be and your mother can throw them out in the evening.
As to where grandmother will live. Unless she has a monthly income of $3000_$5000 she won't be able to live in assisted living. She will need a momtly income of probably $2-3000 to live in affordable senior housing which is subsidized. She may be able to get housing assistance from medicare if she requires assisted living. She will not be able to have her dog with her if he's urinating/deficating inside.
In Portland, there is an office, Senior Solutions, that helps in understanding about and finding housing and other types of care.
I suggest that your mother may have have to be tough and say no dog. I suggest that first she include your grandmother in exploring options. Being a part of the decision won't make giving up the dog any easier but it will preserve your mother's and grandmother's relationship.
Wow! I reviewed your post. Your mom is having knee surgery. Who will be helping her? Is your grandmother mostly self sufficient? I think that if grandmother is unable to do the clean ups herself the dog has to go at least until your mother is on her feet. I've helped 2 people after knee surgery. They needed me for a couple of weeks. And had limited mobility for weeks after. Taking care of her mother's dog is too much to expect. Perhaps you could kennel him.
Your mom doesn't want to be a burden yet she is because of her dog. I suggest she has to assume all responsibility for his care or mourne his lost. It is what it is. It's very difficult to let go but she has to do that.
It sounds like she doesn't have enough money to pay for her own place. Unfortunately she didn't plan and these are the consequences. I urge all of you get into family counseling to help with this major transition. The longer your mom struggles with the dog she will be less able and less willing to have your grandmother there. And......Their relationship will become strained. I know this from my own experiences with aging parents and my friend with her dog.