i think by the majority of people, you have been given an unfair rough ride on this bt some silly people.
i have an 18 month old daughter and whilst i love spendin 99% of time with her, it is healthy to get a break occassionally. My parents love taking my daughter, they almost beg me to go out more often. I know that i am lucky to have parents that i can trust and rely on and that they are happy to help out.
I cannot imagine feeling comfortable with anyone else looking after her. If i did not have this luxury (and i do not go out often, i think i have left her 5 nights), i would cope but the break is healthy and i always look forward to seein my girl the next day, i appreciate her more for the break.
Other than that, i can only suggest like others that you ask your mum, just ask her if their is a time, date or weekend etc that would suit her. if she doesn't seem keen, if you just ask her if there are any problems she will most likely explain the situation and be happy to help out when the issue (whatever it may be) is resolved.
good luck