What if you just put several blankets around in her bed, and she can grab any one of those and put it on her.
Toddlers can be real persnickety... and yes, she probably does not have the fine-motor skills yet... to put it on herself... exactly like she wants it or is thinking. Toddlers at this age, OFTEN cannot yet do... what they have in their heads... because their mental "ideals" do NOT match, their fine-motor or gross-motor skills and ability yet. That is why the get frustrated.
Imagine... if you wanted to paint flowers on a canvas. You watched a TV show about it and 'knew' mentally how to do it... but could you ACTUALLY do it... AND JUST LIKE the Artist on the TV show??? Probably not. Thus, like a Toddler.
Or, explain to her that she can only call you ONE time during the night. That you need sleep too... and a tired Mommy is a grumpy tired Mommy... and you BOTH need rest. That even your blankets sometimes comes off during the night, but oh well. You can STILL sleep fine....
Put a paper on her wall... each time she calls you, mark off a BIG tally mark. The number "1". Then tell her... that's it.
And put about 2 or 3 blankets in there for her.. .and she can use either one.
My son, is recently made 4 years old... he still needs occasional help with putting on his blanket JUST so. But more often than not... he prefers NO blankets on him.
all the best, it must be exasperating!
Susan