I've posted before about my experiences at my Dad's house while growing up, but this is what happened at my mum, mostly to her.
After my parents split up when I was in Year 4 my mum moved into a house, an 8 minute walk away from my dads. Which was good for us to walk between both houses without our parents.
We had a routine of when we stayed at who's houses and it worked well.
Anyway, my mum got herself a new partner and was generally moving on with her life. My mum started mentioning weird things happening around the house but she didn't really get freaked out.
Her main events she still remembers vividly to this day are, once, she was asleep in bed and she must welcome demons because she sleeps with one leg out of the covers and hanging off the bed. She got woken up being slapped on the foot, she said it wasn't painful but she said "go back to bed" assuming it was me or my brothers, it wasn't until morning she realized we were all at our dad's for the night and when she looked at her foot there was a pink handprint. (Her partner was at his house that night.)
Her second main event she remembers is while I and my brothers were at my dad's, she decided to do some tidying while her partner laid in bed watching tv (not being lazy, he was on strong pain killers and needed a lay down.)
To give a mental picture of the landing area, you walk up the stairs, bathroom is directly in front, you veer to the right and there's my brothers' bedroom door with a plug socket next to it, then there is my mum's bedroom door and next to and facing the bathroom door was my room. So, my mum has the hoover plugged into the socket and is hoovering away when the hoover just stops, she notices the switch has been turned off and the plug pulled out. She walks into her room to ask her partner what he was playing and he was fast asleep. Even if he wasn't, there is no way he would turn off the hoover, unplug it, get past my mum unnoticed and across to the bed in the space of 30 seconds.
She's mentioned a few little bits that I can't remember myself at the moment.
The only thing I've witnessed/heard is I would refuse to sleep unless my cupboard door was closed. Which could just be a usual childhood fear.
Also still to this day, after several new kettles, several places moved around the room, the kettle will turn itself on to boil (we have to make sure it has water in so it doesn't break) these are ones you have to flick to turn on and there's nothing around it to turn it on.
Going back to when we first moved house... We did move to a school closer to my mum's house (which still baffles me to this day).
When I first moved schools there was still a "buzz" about a little girl who had been at the school before I arrived who had been ran over and sadly not survived. From what I heard she was moving to a different part of town and wasn't happy about it and stormed out of her new house or grandparents and was hit...
Turns out the girl who died, lived in the house we had moved into, maybe she loved it so much she just wanted to stay and play? My mum never felt threatened, she was probably used to childish pranks with having me and my brothers.
Side story
The only personal experience I've had at my mum's house...
We had a house rabbit called Quo, he was amazing, had such a big personality for a rabbit and we adored him. He was a bit cheeky; if we snuck in to our mum's room to sleep in her bed, he would come upstairs and "burrow" into the cover until we went back our own room. That was HIS side of the bed even though he NEVER slept on it lol. He also used to run around the house having a mad half hour and when he got in front of the sofa where we were sat he would jump up and flick his tail and back legs then carry on running around.
Sadly, we found out he was very poorly, you name it he had it and we were advised to put him to sleep for his own benefit, it was absolutely heartbreaking, me and my bothers were all still 10 years old and under.
We buried him at the bottom of the garden and made him a little gravestone. One day I was looking out of the window as something caught my eye, I saw Quo doing his weird flick dance, around where his grave was, I blinked and he was gone. Never happened again.
I've read about sleeping with a leg sticking out of the bed, my mum swears she felt someone grab her foot while it was out of the bed one night, I just downplayed it to ease the tension.
I do believe that it could be the spirit of the girl your mum encountered, it's kind of sad that she never got to live her life out to the fullest, but it's good that the incidents your mum experienced wasn't menacing or scary.