Today I took a sick day because I was very ill (bad stomach flu) and towards the end of the day, I got a call from my boss. She asked me to call her back, so I did, and she basically said she thought the job was not working out for me. Of course, she gave me an explanation on why, and I was able to make my arguments and get her to side with me on most of them, regarding my training by my mom's old high school friend, who works in the office currently. Of course my mom's friend is knowledgable but her training is not helpful whatsoever. My boss feels that I still have no idea what I'm doing, though this lady has not given me any constructive criticism to learn from my mistakes. So, in other words, she let me go all this time doing my job wrong and failed to mention our boss was not happy with my work/our work. My boss said she would have a talk with her and let me know what she says, but what should I do? Would it be right for me to ask if I return to work tomorrow?
You are fired when they remove you from their premises, not earlier. Don't make any assumptions that might end up hurting you. Even if your boss yells to you at the phone in the evening "you are fired" it doesn't mean that you are fired in the morning when you turn up for work and he or she has calmed down.
There is no reason to ask - let sleeping dogs sleep. Don't remind them that they wanted to fire you; better if they don't remember. If you are fired you will be told. And if you are not told you are not fired.
Meanwhile, it may be wise to look for a job elsewhere. Without telling anyone at your company. (Lots of questions here with good answers about that subject).
I agree with Dawny's answer, definitely go to work, don't exacerbate the problem by not showing up. But would add that it's a good idea to start looking for a new job. Once the idea that you're not performing is given voice, things tend to get worse, because your little issues become bigger under scrutiny.
If it was me, I'd now be looking at holding the current job just until I find another, and focus on doing what I can to make sure I get a good reference from them and leave on good terms. The boss is giving you a chance to do exactly this.
Would it be right for me to ask if I return to work tomorrow?
Did the caller even mention that you were getting fired? No
So, it means that you have to return to your job as usual the next day.
And in addition to your usual activity at job tomorrow, you can also ask your boss for a performance review, so that you can clearly know what you were lacking and can improve on that.
As far as your question goes, I see that the call is just a performance criticism/review, and nothing more. And definitely not for firing.
A lot of good points on this thread. However, one interesting thing I notice is you said this:
Of course my mom's friend is knowledgable but her training is not helpful whatsoever.
Based on that I assume you are a teenager/young adult with his first job? If so, it sounds as if they are trying to be nice with you since your mother set this up for you. If so, perhaps you and your mother can open a dialog with the boss and determine where you are coming short.
Also, I hope you did in fact called in sick today and did not simply not come into work and your boss, worried about you, called you up to see how you were and found out you failed to call in. That would be bad and perhaps it could tie your boss's hand in her having any say in keeping you on the team.