I recently (3 weeks ago) adopted a 1yr old Cocker Spaniel/Pengkinese boy. Some traits that I have learned while having him so far:
Mellow - has energy with other dogs but usually mellow at home
Very loving and cuddly
Very good and playful with other dogs
Obeys sit, lay down commands very well
Not super motivated by treats only high value (baloney, hot dog)
Not interested in any toys (tried balls, squeakers etc)
Either has separation anxiety or still not used to new environment. Will whine if left alone in crate and leave the room but will eventually calm. Initially went berserk when I would leave the house but now settles quickly. Follows all over the house, even whines while I am in the shower and he is outside the shower door in the bathroom. He will sometimes voluntarily hang out alone on the couch while I am in the kitchen but I need to be visible.
Goes potty outside on walks but still pees inside if left unsupervised.

I have a few things I would like to sort out but they are all sort of connected.
1. I want him to go potty in the backyard but he really refuses to go in the back yard. He doesnt even like going out to the backyard because its always so hot out there (live in AZ, always over 100 deg.) and he overheats quickly. The only way he will come outside at all is if I leave the door open and then walk back there out of sight where he will eventually come to follow me. Or I have to carry him out. He then lays down in the shade and doesnt ever go potty. We cant stay longer than 10 minutes or we will both overheat.

We walk 1.5 miles every morning at 5am and 1.5miles every evening at 8pm (when its cool enough). These are the only times he goes potty. I work all day but come home at lunch and let him out in the backyard but he never goes potty. We cant walk at lunch because its too hot. I have carried him to his spots he normally goes when we walk and he will go at lunch if I do that. He will go consistently every time we go for a walk. If I take my eyes off him in the house he has a tendency to pee on the carpet

Last weekend we did backyard potty training - only leashed to my belt, in the crate, or in the back yard (we didnt go for walks this weekend). He went 22 hours before finally going potty in the back yard successfully. He got major treats and praise. Since then he still doesnt go potty back there. Should I repeat this process?

2. Potty training with SA. I have tried the leash method (always leashed to me so I can watch him) but he puts his but down and doesnt want to walk around the house while leashed. I end up having to carry him everywhere. In the crate is fine but if I leave him out of sight he will start to panic a bit. I end up sitting on the couch with him all day and not getting anything done because I cant take my eyes off him or he might pee on the carpet. Id like to have a little more freedom in the house. Should I crate him and ignore the crying? He doesnt get violent in the crate, just crying and barking. I dont want to turn the crate into a negative space. He does enjoy the kong but his anxiety takes priority over the kong if he gets anxious he forgets about the kong.

I believe if I can get him to potty in the back yard I can be more comfortable letting him free in the house knowing he doesnt need to relieve. If I can get over that hurdle I think it will help us make a lot more progress.

Thanks for taking the time to read all of this. I want my boy to be confident and secure and I also want to have some confidence that he wont potty in the house.