Is there any hope in training my older dog?

For complete context, my dachshund Bubby is 4. We got him when I was 15 and really involved in school and sports so my mother took on the responsibility of training him. She gave up really early on and now Bubby is completely untrained besides super basic things like knowing to come, sit, and wait before feedings. Hes a pleasant dog, has some separation anxiety, doesnt tear things up or cause any great trouble but the pottying in the house is killing me. It's embarrassing and completely our fault. Ive tried over the years to train him but hes extremely stubborn and im not always home since I work almost every day. Most training guides advise that I be home at all times with him during training and I swear he wouldve been potty trained already if I had the ability to do so. I always feel so guilty that hes not trained and my house no matter how much I clean, always feels icky. I am constantly seeing people say that dachshunds are super hard to train even as pups so im going into this really discouraged. I know paying for a trainer is an option but its super expensive and still theres no guarantees.

I'm no longer in school or sports but I work mornings from 6-2 mon-fri. My mother also works mornings and shes been no help in trying to train him so its all up to me. I am still living in the same house hes familiar with but planning to hopefully move out soon taking him with me.

bubby will only pee and poop in the entry way of the house, just sometimes in our bathroom and rarely will mark the carpet. The entry way to our house is tiled floor and ive used enzyme cleaners before but not consistently. If we are outside he will hold his pee or poop until we get home. As for reinforcements I dont discipline him because ofc I know that does nothing. Any time he "pees" (hes usually just marking) on grass when we're out I give him tons of praise. Idk if it is because my mother only used puppy pads when we has little but hes just super set on peeing in that exact spot.

So my questions are: is there really much hope in what I can do by myself to potty train him considering my schedule? Will crate training need to be completed before I can even begin to think about potty training? Will it require constant supervison? Are there any other factors that might unknowingly be making it more difficult to train him that aren't commonly brought up in potty training tips? What worked best for you if you've trained a stubborn dog or a similar case? Will it be easier to train him once I move out? or will I just have to bite the bullet and pay hundreds or thousands for a trainer that may or may not even work?

I'd truly appreciate any help I can get. This is only the most bothersome problem I want to start with and i'll definitely have to make separate posts😔