Family is Family and Genealogy is about families and their histories. In creating a family tree it should be an easy thing after all everyone has a mother and everyone has a father - right? Enter the modern world in which you have single parents, same sex marriages and partnerships, multiple marriages, multiple divorces, adoptions, polygamy, sperm donors, a wide combination of half siblings, sex changed parents, surrogate mothers, and the situation of the Delaware Gore Family in which a woman adopted her ex-husband as her child. In other words the non-nuclear family.
Under the old system you didn't mention any relationship that was not a blood legal relationship and if the mother wasn't married at the time of birth that fact was glossed over. It was, let the reader figure it out or let Aunt Beth tell them the facts of life.
Interestingly as late as the early 18th century, among rural farm families, you will sometime find the first child born before nine months of the marriage ceremony. There was a very sound reason for this, namely to insure fertility before marriage was contracted. This was to be certain the spouse was capable of providing an heir to inherit the property and children to work the property in the parents' old age. It may not have been openly condoned, but was well recognized.
Today people want to scream their weird familial scenarios to the world and insist the family tree reflect those facts. If you are using a commercial software problem to do your family tree you will find it is impossible to use or certainly a challenge. Oddly, well maybe not too odd, the Morman family tree software has a utility for polygamy. For same sex marriages there seem to be more commercial programs that can handle this such as Family Tree Builder. With other commercial software the only way to handle it is in the notes section (they usually allow notes on each person in the tree) something like; the mother and father you're tied to aren't your birth parents they used a surrogate mother and a sperm donor so you can call anyone you want you mother or father as those people you presently call your mother and father don't have a clue.
You may have to go to simply using a word program and create your own free flowing tree from that. In all cases however it is YOUR family tree so include whoever you want in it. It may not be recognized by the DAR (Daughters of the American Revolution required you to prove lineal, blood line, descent from an ancestor who aided in achieving American independence) but for your purposes it will be fine.