Cluckity, you have my sympathy. Whilst yes, you did something incredibly stupid by having an affair, it's clear from what you've written that the reasons as to why are complex. Everyone does something daft, or stupid at least once in their lives, and I whilst most of us wouldn't have extra-marital affairs, I suspect that very few would/will sit in absolute judgement on you and this horrible, awful situation. Yes, you're in this situation because of the choice(s) which you have made - and the consequences of that choice are, for you, awful right now. But they don't have to be.
Your husband is abusive.
Leave him. Take your daughter (who you're teaching how to be a wife/girlfriend... and believe me, she will end up in an abusive relationship herself at some point, unless you break the cycle!) and run. Yes, she has the right to a relationship with her father... and that should be facilitated. However. She also has the right to live in an environment which isn't abusive. So do you. How do you think your husband is going to react when he finds out that you're pregnant as the result of an affair? Because if you can be so certain that the pregnancy is the OM's, then that means your husband will know, without doubt, that it's not his, too. If you have a termination, you will carry the feelings of shame and guilt that are currently consuming you for the rest of your life. You won't be able to talk to anyone about it, because no one in your life will know about it. It will be your burden to carry alone. I wouldn't wish that on anyone. If you don't have a termination and continue the pregnancy, then your husband's abuse will ramp up - towards you and your child(ren). Would you wish that on yourself? On your daughter? Do you truly believe that is all you are both worth? Because you're not. She's not. So run, before your husband's physical abuse ramps up.
As for the "other man"... well. You were a boost to his ego, he's told you who he actually is (so listen to what he's telling you!), he's pushing for a termination, when he actually has little-to-no say in the process of you making a choice about your body, and he's shown only the same amount of concern that a total stranger would for someone's health (ie, extremely little, and actually I'd say "none"). He's not going to be there for you if you have a termination and he certainly won't be there for you if you don't, I'm afraid. I'm willing to bet that he's only hanging around because he wants you to terminate and perhaps is even bullying you towards it, irregardless of what you want to do regarding your body and your choices/options.
I suspect that you had the affair because you were desperate to feel loved, needed, appreciated... everything which your husband no longer makes you feel. You say that you come from an abusive family background... and now you're replicating it for your daughter, whether you realise it, or not. You have to acknowledge that this situation, this set-up isn't good for the child you already have and that you have to change that - for both, perhaps all three, of you. The "other man" is also, I'm afraid, subtly abusive towards you - emotionally, at least. And he is by no means innocent in this. You might be married, but he chose to have the affair with you, knowing that you're married. You are equally to blame/at fault... but you're the only one who will end up hurt by whatever happens next. You have another choice to make, which will have consequences that, one way or another, will reverberate through the entirity of the rest of your life. Please make the right one.
And leave your husband.
I am a single mother to two children with no support whatsoever. I don't receive any financial support from my DS' father... just as I didn't from my DD's biological father. He's been absent since I left him when I was pregnant... because, like you, I was in an abusive relationship. Pregnant. Being pushed to terminate, even though I didn't want to. And my parents are dysfunctional without the "fun". My son's father was also emotionally abusive (and very like your "other man", I suspect), so believe me when I say that I can spot the signs a mile off. If I can be a lone parent with no support... then anyone can. Yes, it's hard. Yes, it's difficult. Yes, you'll hate yourself for breaking up your child's family. And yes, it is/can be exhausting when you're the one who ends up doing absolutely everything for your child(ren). But being free from abuse, knowing that your child(ren) is safe from it... makes it all worth it.
Whatever you decide, I truly and very sincerely wish you luck - and hope that you not only make the right choice for you/your daughter, but come to understand that we cannot rely on anyone for our own happiness (in other words, be single for a while, learn to love yourself, learn to believe that you're worth so much better than your husband and the "other man") 