Nannytothequeen spot on! Op accepts the mistakes she's made and is trying to rectify them.
Those of us that have actually been through this know how much it hurts and humiliates.
We know how it affects our kids too, to think or claim it doesn't is incredibly naive and disingenuous, not just the affair but seeing their dads start new families that they live with, spend far more time with, give more care to, invest more in not only in money but most hurtfully in time and love.
I have tried to support dd through all this, reassure her that her dad loves her (which I believe he does, but he does a really shit job of showing it!), that she is NOT unloveable. Yep they often feel that way, this is something I've discussed with people in real life who've had the same experiences and it really screws the kids up even if the dads are reliable on contact etc these kids still feel rejected, "less than" their half siblings, unwanted.
As a mother it's incredibly painful to see your child go through that, to question their value as people, to wonder if anyone will really love them romantically, to struggle to trust anyone romantically (because they know better than most how badly it can go wrong), hell even struggle to trust friendships not because they don't trust their friends but because one of the first people they should have been able to trust would always be there for them wasn't.
And I never see any of these dads acknowledge or take proper responsibility for any of this, they usually blame the mothers! The ones who HAVE stuck around, raised the child as best they can through all this, who've gone without so the kids don't, who've worried and soothed and comforted when that child has been let down yet again because being a fully present father was just inconvenient.
It's disgusting and generally speaking these men don't get anywhere near the vilification that single mothers do.