Potty Training a 3yr jrt

Question
About 2/3 months ago i adopted a 3yr old female jrt called titch. When i got her i was told she was spaded which i believe is un-true as she was bleeding for a fortnight or so. I am taking her to vets to check soon.
However the problem is potty training her. I know all the main rules such as no telling her off after she has done it and only when we catch her in the act can we shout at her, but we never catch her. I have done much research and i have been told the crate option is best but I do not think this would be fair to do as because of jobs we can not always been around through the whole day so she may be in there for a long length of time. When we are in, we leave the back door open so she can go but she just doesn't, also before we go to bed at night we take her out but she will still go through the night regardless.Any other techniques would be great or are we too late to teach her anything?

Answer
Good morning,
It's never too late so don't give up hope. Unfortunately the best thing to do is to start completely over. It's going to be hard but it's the only way that has ever worked for me. You have to treat her like a new puppy and take her out every hour on the leash around the clock. When training my new puppies I even do this throughout the entire night. I know it sounds crazy but it works and it stays with them forever. Your dog is older so she will be able to "hold it" longer during the night and probably isn't necessary to go out all night.
You're right about correcting. It's useless to correct after the mistake has been made - just clean it up and go on with your day. However, when you do take her out and she does her business outside where she is supposed to, you have to LAVISH her with praise, almost going overboard with it. You are sending a positive reinforced message to her brain and you have to continue this praise over and over every single time she goes where she is supposed to. You can even use cheese or a little treat to reward her when she does it. When you take her out on the leash, you need to be in a serious state of mind... no playing, etc, you are out there for a reason. Use a one or two word command to say what you want from her and then praise like crazy when she does what you want.
For example.... I use "go pee" (how original of me!).
OK, so to go over this:
Take her out on the leash in a serious manner, say your command, and praise praise praise like crazy when she does her business. Then RIGHT BACK inside until the next hour.
It takes puppies about 1 week to 10 days to be fully trained and an adult dog could learn it quicker.
I understand you work which makes this technique a little more difficult, but do the best you can with it while you are at home. Praise works wonders.
You might want to consider hiring a neighborhood kid to come in during the day to continue this training, at least until she fully understands. Even if you don't have someone come in that often, it's healthy for someone to come in at least once to let her out.
Definitely take her to the vet if she was bleeding. Usually when dogs are in heat, they bleed for at least 10 days. You'll have to go buy a doggie diaper and some pads or you will have blood drops all over your house. That was unfair  of whoever lied to you about her being spayed. Unfortunately it costs more to spay a dog that has already been in heat. Keep your patience high and she'll do fine.
Best of luck to you and Titch!!!!