1) Actually your analogy refers to a trespasser, i.e. an interloper interfering with one's person or property. A trespasser does not have to be a stranger, it can be anyone known or unknown to you who interferes with your person or property.
2) In a state of nature, the individual will act as they so choose in how to deal with such an interloper. The law (a social construct) merely recognizes and supports this right of individual action by setting parameters to prevent unnecessary harms.
3) Now here we get into semantics, since both terms have various definitions depending on the user's viewpoint.
4) To some, "Mother" refers to the female whose egg was used to conceive, whose body was used to give birth, and who then raised the child so conceived. But that's a bit hazy since we currently have forms of surrogate which mix this process up, not to mention usage in adoption.
5) In biological terms, the word "Child" refers to a human being after birth (when childhood starts) but before puberty (when adulthood starts). Socially the term applies to persons born to, or adopted by one or more adults who identify themselves as parents.
6) I raise this point because when you used that phrase "Mother's obligation to her child" you are clearly trying to imply a social or emotional link which colors the viewpoint; thereby obscuring a clinically objective argument. :shrug:
7) In answer to the first question; YES, you need to throw out your construct in order to try to discuss the issue objectively. Otherwise your emotional haze will interfere with a rational analysis.
8) Instead, being an OB/GYN, you should be looking at this biologically. That childhood begins at birth; while the processes occurring between conception and birth involve phases of development leading to the potential creation of a human being. I use the term "potential" because as an OB/GYN you should be well-aware of the possibility of natural miscarriage at any stage prior to actual birth.
There is no correct answer to your second question. That is because "right and wrong" are moral choices, with few (if any) universal absolutes.
9) For example, to a Hindu it is morally wrong to kill any living creature, while most other cultures think it's perfectly okay to kill just about anything other than a human being if it suits our needs, while there are some belief systems unconcerned about human life. So when you ask this question, that remains an individual choice based on one's own belief system. :shrug:
10) The last question is key, should abortion be illegal? IMO, the answer is a resounding NO! This because using the purely biological rationale, the cells are going through several stages of development in the womb before they become a human being entitled to legal protection.
11) They are human cells; but they are not developed from inception with enough attributes to indicate viable individuality. This does not occur until some later point in the process. So like any other group of human cells in our fully developed bodies, they may be dealt with medically as needed or desired by the human being carrying them.
12) If I have cancer, you can cut it out even though they are living human cells. If I want to donate a Kidney, or part of my Liver, I can elect to do this even though they are living human cells. Women should have the right to decide what to do with this developing potential right up to the point science can determine potential has turned into actual human consciousness. At that point, this new human being deserves some protection under the law.