Plot hole: They aren't able to travel before the birth of their children or their children become different. Despite that, he visits his father one last time before their third child is born. His Dad and he then travel back to when he was a kid, which would have changed his first 2 kids.
About Time (2013)
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Directed by: Richard Curtis
Starring: Bill Nighy, Rachel McAdams, Margot Robbie, Domhnall Gleeson
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Suggested correction: This is not necessarily inconsistent with the movie's time travel logic. Since Tim goes back in time to visit his father and inside that particular time travel, they use time travel to go back to a day where Tim was a child. Then, they return back to the original time travel where they're playing ping pong. At that moment, both of Tim's kids were already born. So, when he returns from the ping pong scene, there's no change regarding his kids.
Also, paraphrasing the Dad, he said they aren't going to change anything. It is more like reliving a memory than changing the future to get what you want. The Dad couldn't go back to not smoke before his kids were born because that was major and would have changed the course of his life; walking a bit differently on a secluded beach that you walked on in your younger days (as long as you spent the same amount of time - presumably) would not alter the trajectory of one's life.
The slightest change in 1 second of being on the beach would absolutely affect his kids. A man produces 1500 new sperm every minute. Altering the timeline and delaying every event that is going to happen by literally 1 second would most definitely alter which exact sperm was used when conceiving both of his first two children.
Mary: I'm going to go into the bedroom and put on my new pyjamas, and in a minute you can come in and take them off.
Trivia: This is Rachel McAdams' third time travel film (she also stars in The Time Traveler's Wife and Midnight in Paris), but her character hasn't time traveled in any of the films, it's always someone else.
Question: Whenever Tim goes back in time, his clothes change to whatever he was wearing at the time, but he always appears in the same spot that he left from. Both times he goes back to the NYE party he appears in the upstairs wardrobe. So what happened to the version of him that was already walking around at the party? Did that version of him just vanish?
Answer: This is one of the (many) time travel plot holes in the film, and unfortunately your question doesn't really have a definitive, or satisfying, answer. Richard Curtis has said he was less concerned with making an airtight time travel film than with the human story at its core, so he let things like this slide without explanation. However, since we don't see any "second" Tims around when he goes back in time, and no-one else seems to think of him as an "extra" Tim, we can safely assume that, yes, he replaces himself in the timeline when he travels back. (Of course, this doesn't explain what happens when he then returns FROM the past).
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