I can't tell you what to do. But you already know what you want to do. You told me "I regret cheating, I don't want to lose my family". There are a few things I would suggest you consider:
Couples counselling for you and your partner. Assuming you meant what you said about your family, you will need to break up with Judith, you can't see both women, though loving both is quite possible of course, love for one is entirely about that person and they are individuals. I think you will need to accept financial responsibility for the baby, but you have to consider if you want to involved in any other way. The risk with that is that you jeopardize your family relationship because you are still "involved" with the other person. I understand that you may feel it is unfair to that child for you to not be there to look after him/her, but your girls were your primary commitment and they still need you. This is also how the law sees families, where your first family comes first.
I am not telling you what to do, just making you aware that being a dad to two families, if you still have feelings for both partners, is obviously fraught with issues. It's usually somewhat different when people get divorced as they move on with their adult relationships (although this can still cause problems). Only providing financial support to Judith and the baby will allow her to find someone she can love (without constantly seeing you) who is available to her and will prevent any...relapses in your mistake, because we're all only human.
Whatever you choose, the problems between you and your girlfriend need to be resolved and counselling is often a good place to work out what has gone wrong and why.
I would speak to a separate counselor alone, before you both go to different couples counsellor; for counselling to work out when you should bring up the infidelity. It may be that if you bring it up immediately it causes a rift and difficulty in resolving other issues. It may be prudent to wait to tell her what has happened until after you have got back a stable foundation and dealt with why your arguing and getting on each other's nerves started.
Healing in relationships requires 100% commitment and effort from both parties, you can't be looking outside to find others or leave. If you aren't willing to give that to your girlfriend and family, then I can say that your chances of success are low. I wish you luck. I can't say it will be easy. I can say that a healthy loving strong relationship, where you've worked through those issues together is IMHO (in my humble opinion) worth it.
All the best,