When you talked about "wanting to share the happiness around", you were referring to the source of that happiness as being the MC & then you suggested that adding cheating will supply Lucy with some happiness.
Having just said that you "will do whatever it takes to bring her some happiness." The implication is clear.
You used your MC's "caring guy" persona as reasoning for why you can see cheating in the game's future.
Cheating is not caring for anything but your own gratification.
"I know you're damaged & trusting me was a huge thing, but I only fucked your sister & betrayed that trust because I'm a nice guy & didn't want to hurt her."
Yeah, that's gonna work out well.

Well, mine is based on how the characters and the story have been set-up.
Yours seems to be edging closer to a wish list scenario, or turning the MC into a disloyal, dishonest cheat, which is completely out of character.
You say you do not want to hurt Lucy, then propose something particularly hurtful to her family &, by extension, to her
She'll get over being rejected by the MC. She's perfectly capable of meeting someone.
She won't get over being rejected by her sister and her nieces, losing her family & having them lose trust in her.
Not to mention the guilt she'd then carry, for having played a part in ruining her sister's happiness.
If you do not want to hurt Lucy by rejecting her, then perhaps commit to being with her exclusively & make her feel truly special.
Fucking her behind her sister's back is absolutely not the answer.