Well, the nipple twiddling is so common in nurslings of this age that I believe it is almost instinctual.
thismama, I can so relate to your feeling drained and not wanting to deal with certain behaviours. I do have a partner, and yet I still feel this way sometimes. And toddlers are a tough age (wait until 3, that is even tougher) in terms of how they play on your emotional energies. Babies just seem to require us to get less sleep and use more physical resources, but toddlers and older children need emotional resources, and those are tough for many of us to dole out, as many of us have not dealt with all our own issues, kwim?
Which leads me to saying that it's okay for you to feel this way, but I don't think you should use those feelings as a justification for a certain discipline technique. It's YOUR issue, kwim? And actually, you might find that the path to more patience and greater happiness with your parental approach lies not in how you deal with your DD, but how you deal with yourself. In this light, I would totally recommend Becky Bailey's book "Easy to Love, Difficult to Discipline". It's a misleading title, I think, because really it's about what WE bring to parenting and how we can make changes to ourself that make parenting so much easier.
And let's face it, it's probably easier to change ourselves than to try to go against the nature of the child. Plus, the benefits extend to other relationships in our life as well...
As for your DD "testing", well....I think you are on the right track, and you may think that what I'm about to say is too small a distinction, but I still sense an "adversarial" tone to your attitude about what your DD is doing. You state that you understand it's developmental and about her individualizing her sense of self, and yet you repeatedly stress the fact that she's doing these things "because she knows they are no-no's". Not only does this place an adversarial tone on the behaviours, but I think if you really thought about it, the distinction of being "no-no's" lies in your own perception. For example: does your DD like to play with toys? Does she enjoy repeating the same maneouver with toy, like pushing a button to make a sound or an object pop up? Does she repeat that again and again? And yet, that isn't a no-no. Watch her play - I'll bet you see the same exuberance for freedom, the same stubborn determinedness, the same emotions...but because they are taking place in the context of "acceptable" situations that don't impact what you are doing at the moment, you don't see them the same way. But turn that into pushing a dryer button over and over again or running out into the street...and suddenly you see it differently. What we perceive is very much "in the eye of the beholder". While I don't hear you directly ascribing sinister motives to your DD's behaviours, I do hear an interpretation of her behaviours that you are using to justify punitive/consequence driven parenting, when I think the distinction is artificial. Does that make sense?
You said that you think responding by playing with her might be reinforcing the behaviours, and yet there is evidence that such a behaviouralist view of children is flat out wrong from a biological and psychological perspective. Yet it's hard to get past behaviouralism because we, as a society, have swallowed that so deeply. Anyways, I urge you to read Alfie Kohn's Unconditional Parenting, as he addresses the history behind behaviourism and how much evidence there is that such interpretations are very misguided.
oh, and props to you for going to school and doin' the single parenting thing. i have much respect for mamas in your shoes.