The sentence is ヘニャッってなりたくなる. I can't find its meaning.
I agree with Chocolate that it is 擬態語. Thus if I understand correctly it is a sibling of onomatopoeia, but not quite the same thing, because ヘニャッ doesn't come from sound.
The mental picture this word should evoke is something soft that buckles or collapses. So in the context of what you provided, I think it's a (tired) human body that buckles (onto the lap of the girl/boyfriend or something like that I'd imagine, since you say 甘えたい)