AITAH for lying about my schedule in this situation?

For context: I am a woman who is almost 30. I am a single mom. My son is 18 months old (a year and a half). He is a toddler.

My mom babysits my son when I work. No, me and my mom DO NOT live together. She just babysits my son at my house.

She has a habbit of getting here late when I need to go to work and then it causes a domino effect of me being late for work. My kid is not old enough to be home alone obviously and I can't bring him to work with me either. I also walk to work since I don't have a car. But luckily my job is close enough to my house to where its fine. My store is litterally less than 1 mile away.

One of my bosses had a talk with me about me being late yesterday. And he told me I should try to get to work earlier than scheduled so that I am not late.

Today I was suppose to be at work at 1:30 but I lied and told my mom that I was actually suppose to be there at 1:00. I told her that so that I can be sure that she gets to my house on time so that I won't be late.

My plan worked. She finally showed up on time this time and I was also on time for work. But when she got here I (sort of) fixed my lie and said "I actually go in at 1:30 but I thought it said 1." Then she had an angry face expression but did not say anything. (The reason I corrected my lie when she got here is so that she did not assume that I was late when she saw me leave at a later time than what I told her)

Whenever I am late I stay at my shift a few minutes longer to make up for the time that I missed when I was late. I do it to make it up to my boss and also to make sure my paycheck is not shorter from being late.

Well today my mom sent me a text saying "Please make sure you leave the store on time today. There is a bad weather warning." (The weather is actually fine. But appaerently there was a tornado warning. But when I walked back home after work, the weather was fine. And the weather was also fine on my way to work too.)

After I got back from work my mom spent at least 10 minutes talking about something else and when I tried to add to the conversation she kept interupting me and said "I have to go. I have to pick your sister up from work." Okay, so if she was in such a hurry then why did she just waste 10 minutes talking about something when she could have just waited to tell me about it later on the phone instead?

After she spoke to me for 10 minutes she also added that her 2nd car stopped working. I asked her "When did that happen?" And she told me it happened today. (She and my step dad share 2 cars. They each use one for when they go to work or for when they take my sisters to work.) I then asked her if she will still be able to be here tomorrow (cause I work again tomorrow) and she said "Yes. I will figure it out. I should be here tomorrow." But when I asked for more details she just kept saying "I have to go. I have to pick up your sister from work." (My younger sisters still live with her. But me and my older sister do not.)

I fear that my mom might ask me for screenshots of my schedule to make sure I did not lie about it. But I only lied about it cause I was tired of her making me late so often. I also caught her spying on me at my job once (this was a month BEFORE i lied about what time of I go in.) But when she spied on me that one time she found nothing wrong. She saw me working my butt off since the store was busy and she just happened to be spying on my during rush hour. But the fact that she felt the need to spy on me when I did NOT lie about where I was or how busy my store was is odd to me. I did not give her a reason to spy on me. Therefore, I don't understand what exactly she was trying to find or "catch" me in. But at least she realized that I am a hard worker after she saw me working... and that I never lied about where I was.

And before any of you comment "You are horrible for using your mom for free childcare." 1) I use to babysit my younger sisters for free for her all the time a long time ago when we were younger. 2) she also had lots of free help from both sides of the family when I was a kid. 3) after my son was born the workers at the hospital asked me and his father over and over if we have help from family. 4) I am currently not recieving any child support. I filed for it 6 months ago and they are saying "They can't find him." Which is weird since I know I put the right address on it.