The particle は adds sort of exclusivity in a negative sentence.
For example,
ビールは[飲]{の}まない。
implies this person might drink other alcoholic drinks, but not beer. ビール is singled out to stress that he doesn’t drink beer.
On the other hand,
ビールを[飲]{の}まない。
has no such implication.
When it’s a verb that is to be singled out, it takes the following form:
[V ます-stem]-はしない
Your first sentence follows this pattern. The verb is [戻]{もど}る, so the standard negative (i.e. without は) would be:
二人の愛はもどらないけど
(*) もどりしない is ungrammatical.
The second sentence uses the same は with the たい-form of a verb, [憎]{にく}む.
The formula could be generalized as follows, but this means the same as simply inserting は before ない, as you correctly sorted out.
[V ます-stem]-たくはない
She may have many different feelings towards him, but she at least doesn’t want to hate him.
The ない-form of a verb can also be singled out like that, to form a double negative, such as:
ビールを[飲]{の}まなくはない。
This person does drink beer, but he doesn’t particularly willingly do so.
Both the たい-form and the ない-form of a verb follow the same conjugation pattern as an い-adjective.
Here is an example with an い-adjective.
おいしくはない。
It may be OK (まあまあ), but you cannot say it’s tasty. The quality of tastiness is specifically negated.
Curiously, there is no special construction for a noun or a な-adjective as their negative form already contains は.
[好]{この}みではない。
[好]{す}きではない。
In speech, で is somewhat stressed if the exclusivity is intended.
To make this meaning clearer, you could say:
[好]{この}みという[訳]{わけ}ではない。
[好]{す}きという[訳]{わけ}ではない。
This also works with a verb or an い-adjective, except という is optional in these cases.
[戻]{もど}る（という）[訳]{わけ}ではない。
[憎]{にく}みたい（という）[訳]{わけ}ではない。
[飲]{の}まない（という）[訳]{わけ}ではない。
おいしくない（という）[訳]{わけ}ではない。
Actually, this function of は is not limited to a negative sentence.
ビールは[飲]{の}む。
implies this person might not drink other alcoholic drinks.
