Here's the problem. I don't want to have the possibility of my mc meeting himself so the time machine is a time rewinding device. So...
Is that a viable way to avoid my double trouble?

I've also read stories where it takes a major disruption of the time line to cause a change, as TIME resists change--perhaps this would work for you. Time resets each time he returns to his present.

Or there is the multiverse of infinite timelines. Each time he goes back he creates a new timeline, but when he returns he returns to his own present.

Then there are stories where time travel merely is part of what actually occurred (e.g. Moorcock's BEHOLD THE MAN); and others where one cannot know for certain what even small change will alter the timeline (e.g. Bradbury's A SOUND OF THUNDER).

Btw, one of the best time travel stories I recall is David Gerrold's THE MAN WHO FOLDED HIMSELF.

His time travels would never overlap, at least until the date of her death pushes up to the present day.

Incidentally, he would have to leave later and later from the present to avoid running into himself in the present.

Of course this depends on how much time passed between the events. If he lost her in his twenties, and he goes back when he is forty, he would not be seen as the same person.
I assume he became a doctor learning about her condition. it would take him some years to reach the point where he could help her condition so there is aging there.

He might go into the room at times the hospital is not open to the public or to visitors. That would make sure he does not meet himself.

and some solutions as to why she still dies, is that he misdiagnoses the illness and does not realize that until too late. Or, she has a bad reaction to the medicine he gives her and dies from that. It could be that while it is the right diagnosis and medicine, she has a complication, a second condition that reacts badly to the medicine.

I have read some stories and books with this problem, the writer usually seems to ignore it. That by the way includes me. I have as story about a guy who keeps going back in time to keep his wife from --hmm, not sure how to politely say it so I will say-- flipping out. She attacks him and has to be institutionalize. He keeps going back in time to figure out what caused it and how he can fix it before whatever went wrong goes wrong.

But he never meets himself. Either the writers ignore that problem or they think like me. The last time he went back in time it was from a different time line so in the current time line he never went back in time so he can't meet himself. In my story, in each new time line he has to figure out how to go back in time again even though towards the end he figures out that it wasn't his first trip back.

quote:

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Could the time travel be such that his consciousness is reinhabiting his prior self? Perhaps in your world, that is the only way time travel is possible, where matter doesn't travel back, but only the soul -- and a body is required to make the transfer.

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If the prior consciousness was also in his prior self, there could be some interesting conflicts between the two. If it wouldn't work for this story, it could still be an interesting approach.

Wonder if it would work for a writing challenge?

This reminds me of The Time Machine. (The movie made a few years back, not the book.)
Might be worth checking that out if you haven't.
Also, a little of The Time Traveller's Wife.

The easiest solution would be the multiverse idea mentioned above.