Dubious phone call - What happened?

This story going to be a little bit long (I live in Europe BTW)

Today there was one dubious phone call my mother received. At 9:38 am my mother picks up a phone call from my sister, which is currently in another country (1000km away) . The connection is quite bad and my mother just hears her saying "Mom mom! (not panicking, just like trying so say something real quick) with voices/hissing in the background. It was clearly my sisters voice. My mother tells her the connection is too bad and she will call her in a minute. My mother tries to contact her again and nobody answers the phone. My mother went on to do some things in our house, cleaning etc. and 5 hours later my mother calls her again and my sister answers. My sister says she never called my mom and had no problems, she is fine and studying for university. A little small talk and my mother hangs up. Then she proceeds to ask me "who called then?" Now I checked the call logs.

I have a few questions here and don't understand what happened: 1.) As it turns out, at 9:38 am the call came from my dad's phone (where I checked the logs too and the call to my mom appears there). The thing is, my father was in the same room as my mother when the phone call happened and his phone was on the table. So, the call came from dad's phone, while being inactive (display was black) atm, and it displayed my sister's name on my mom's phone and my actual sister's voice was at the end of the line. 2.) After a little bit of research, I found out it is called spoofing, where you can call somebody and it will display a different name on the receivers phone. Still, how can my mother hear my sister voice saying something with background noises and my dad's phone being inactive? 3.) I wrote my sister over WhatsApp and she told me she never called my mom. She doesn't understand either how my mom could hear her voice. Either way, she also sent me her phone logs and no phone call was made. But there is more. My sister says she received a pop up message that my mother called her at 9:41 and she missed the call. The problem here is, this message isn't displayed in the call logs of her phone, it just appears when she enters airplane mode (which she does often) and gets the pop up message. How is this possible? She says my parents phone might got temporarily hacked, which I think might be possible.

I went through some possibilities: I checked if the names were incorrectly stored in both phones. Sadly, both phones receive phone calls from each other and display the right names. It also couldn't be a prank from my father, since he is, what people would call it, a boomer and can barely understand new technology and has a hard time using smartphones (only uses it for the good camera) My sister also couldn't be joking, since she is also not keen with technology and couldn't set up something like this, also studying for university she wouldn't have time for smth like this.

To sum it up/tldr: My mother gets a call from my sister, she hears her saying something, connection is bad, she hangs up, my mom calls here again and nobody answers. Later my sister says she never called my mom. The logs show the call came from my dad's phone, which was in the same room where my mother got the call,but my sister's name got displayed on my mothers phone while my mother could hear my sister's voice for a short period of time

Just want to know how all of this is possible and what caused it/an explanation)?

Sorry for any mistakes in the text, if you have any questions for more information, ask me.

Edit: Any calls to my sister are smooth and the connection is absolutely fine, so it adds to the mystery why the connection suddenely got bad