Well as i said up thread and was jumped on,, i totally I understand how you feel about allowing your little one to stop overnight, especially as your original post said there were pictures of her on Facebook with people you didn't know. I didn't let any if my children Stay away from me until they were a lot older than 2.
Yes it's with her dad but op doesn't know his family that well.
I assume you didn't marry him so I think all the parental rights are with you actually, why can't dad visit dd at your house or take her out for days but return at night.
Your mom needs to stop arranging things, that's your job.
Definatly get help, keep on at uni studies and perhaps look at moving out from home as soon as you can.
To be honest op I thought from your posts you were a lot younger than 25 but motherhood is bloody tough at any age.
And on dd calling you by your name and not mom, don't worry, my kids called their dad D for years, no idea why to this day.
Good luck