Late response but I think I'm going to argue that line of thought.
You act as though a child and a mother are two separate entities - but while two men don't share any relation that would give them any rights to violate the freedom of the other person, a child and its mother are by default bound in a dependent relationship. Nature made it so that the fetus depends on its mother in the first stage of its life in which it is not able to provide for itself. It's a mechanism necessary to ensure the survival of the offspring which in turn is necessary for the survival of a species. What gives the fetus the right to breach the autonomy of the mother?
The mother does. When the mother exercises her freedom of choice in a conscious act that results in a pregnancy, she willingly puts her independence on the line. (This is notwithstandig rape, obviously, but rape doesn't constitute the majority of what we are talking about, thankfully. As this is a discussion of the fundamental ethics, cases of hardship are excluded.)
When a woman has an abortion, it is only after she got pregnant. I feel like that is often forgotten. It wasn't forced on her. It may have happened because of negligence or ignorance or lack of education or indifference ("When I get pregnant, I can always get an abortion") or bad luck (a busted condom maybe - rarely as it happens) but the first step is almost always one of deliberately taking action and both woman and man are not without fault regarding whatever comes out of the situation - the only innocent party in all of this is the fetus.
The analogy you gave with the toddler and the mother outside of the womb applies to cases where the mother risks her health or even her life by giving birth. That is an exception to the rule, not the rule itself, same as with rape etc. The criteria for abortion is a different one in those cases. Generally speaking, a mother doesn't have to sacrifice herself for her child. She might do it because of a maternal instinct but she has no obligation to.
Maybe I'm just in favor of someone bearing the consequences of their actions, thoughtless as they may have been, and not passing them on to the fetus.
Plus, in societies nowadays you don't even have to provide for the child once it's born. There is a thing called giving it up for adoption.
However, every case is different and I cannot and will not judge people who do whatever they feel is best in their situation. Personally, I am opposed to abortion (except in cases of rape or the mother's health being at risk) because it seems the easiest option out of something that is self-inflicted. And because we are dealing with life, existence and other abstract ethic dimensions, it's fairly problematic. But every woman should have the right to choose for herself. You cannot decide something for other people where there exists no universally applicable formula.