It sounds like you are in the middle of grieving the loss of your wife, and that Sparky helps you with that pain. I do not think giving her away is a good option for those reasons.
There are some things that could help you:
1. Remember the nature of dogs: They sleep a LOT and can be content to be left alone for a number of hours per day (this varies with type/temperament of dog). Dogs are den animals, and like small spaces to go to sleep in, like a crate (you don't have to shut the door). How long are you leaving her alone for? Some dogs (especially smaller ones) need to be let out more often, some can go for a longer stretch.
Just because you feel like you are abandoning your dog does NOT mean that she feels that way! It seems like you need to objectively evaluate the situation.
Is she chewing things up? going to the bathroom on your floor or furniture? If these things are NOT happening, then there is a good probability that she's actually OK while you are gone.
You could use some kind of APP even from your phone to watch her and check in on her --I'm not an expert on these kinds of apps, but I know people who use them.
2. Think about whether or not you have jumped into a new relationship with a girlfriend too quickly. I don't know your circumstances, but if your wife only left you a few weeks ago, perhaps it was too soon? You'll need to think about this one. Even if you had a bad relationship, you still need to go through the process of grieving.
If it is an OK time for you to have a girlfriend, I hope that you would have one who can understand that you are recovering from some issues (the drug use/drinking) and need the extra support that Sparky brings to you. I would hope that anyone that you are in a relationship with would be patient and understand that you need this right now.
Please feel free to follow up with me.