Sounds as if your story is structured more like a classic quest-type story. The hero/heroine has a goal (getting home again), and encounters many obstacles to that goal. He or she overcomes each one as it presents itself, then moves on. There isn't necessarily one antagonist who dominates the progagonist's life in these stories. The protagonist in a quest story is beset with problems they must solve, so the story is never dull. But that kind of story doesn't need a particular character to work against the protagonist the whole time. An extremely good book that might be of use to you is this one: The Writer's Journey: Mythic Structure for Writers (third edition) by Christopher Vogler ISBN 978-I-932907-36-0 I would advise you to buy a paperback copy rather than a Kindle edition, because you will want to be able to easily page back and forth while using it.
Amazon UK carries it. I would advise you to take a look at the Look Inside feature. The Table of Contents is particularly useful. https://www.amazon.co.uk/Writers-Journey-Mythic-Structure/dp/193290736X/ref=sr_1_1?keywords=Christopher+Vogler&qid=1563009651&s=gateway&sr=8-1
Then your main antagonist is what/whoever tries to prevent him getting back and with whom the main resolution in the end will be. It can be a character, a decease, an idea, some lack of ability... I definitely agree with jannert in this:
Ah, so there lies your problem – your protagonist does not have a true “character arc” (at least not yet). Your protagonist has a goal, which is “getting back home,” but “getting back home” is not an arc. For clarity, here is the definition of a “character arc” (from Wiki): “A character arc is the transformation or inner journey of a character over the course of a story. If a story has a character arc, the character begins as one sort of person and gradually transforms into a different sort of person in response to changing developments in the story.” This is why I use caps a lot when referring to story-building terms. While the words themselves are basic enough, there is often more complexity to the meaning behind them than one might think. I assume your story is intended for children/young readers, so your protagonist doesn’t need to have a deep/complex inner journey, but your protagonist needs to at least “change” in some way – that is your “character arc.” For ex. It can be as simple as, your protagonist hates her home, but after the journey, she realizes home is a wonderful place. Or (since your story is about time travel) your protagonist hates the time period he lives in, but after the journey, he realizes it’s a great time in history. Whatever you decide it is, make sure to reinforce this change/learning process in your protagonist throughout your story. Another words, shape your story around your protagonist’s “character arc.” You can do so with more than one antagonist, but all your antagonists should contribute to your character’s change in some way. Any antagonist that don’t do this can be removed without really impacting the overall story. This is why we say it is the protagonist that needs to hold the story together, not the antagonist.
Returning home is the main goal of the character. There is character arc in the story ( it's a apart of the plot that need more work in the second draft.) The protagonist relationship with his younger sister is part of the story. ( they bicker and don't really get on to begin with.) Another is appreciating what you have.
Great! Then quite simply, as long as both your antagonists support this arc, you should be fine. Ideally, your second antagonist should be the stronger of the two that pushes your character to make this change.
