Wishes folllowed by 'that' are expressions of regret for a situation that will, does or did not materialize. The non-materialisation is shown by a backshifting of tenses similar to that in hypothetical conditional sentences.
1. I wish she wouldn't come back.
2. I wish she didn't come back 3. I wish she hadn't come back.
1. Wishes with 'would' express the speaker's regret that something
will (or will not) happen - i.e, in the future and/or that somebody else insists on doing.
2. Wishes with the past simple express the speaker's regret that something
does (or does not) happen.
3. Wishes with the past perfect express the speaker's regret that something
did (or did not) happen in the past.
4. I wish she won't come back. This is unnatural for most spealers of
BrE. If there is any posibility of her coming back, then 'hope' is used.