Really sorry to hear your story of being deceived by your husband.
You did well to get sole physical custody. I was told the same thing about legal custody and was able to get sole physical custody. This was so important to me as I had been a good, faithful wife & a great mom to our kids.... I felt I had done everything "right" and honored my commitments... only to be robbed of my family. He bailed on the marriage & yet I was expected to hand over my kids every weekend. Living here & living there didn't seem like the best thing for my kids, and I was concerned about who/what they would be exposed to. I fought hard for physical custody with a very undefined custody-sharing arrangement. I talked to my husband as we were divorcing & confronted him on how his lifestyle made it unrealistic and unsafe for him to have the kids part-time.
Our arrangement is that the children live with me, their home is with me. Our door is open & he can join us for any school event, dinner, or holiday. My ex and I have good communication about upcoming events & plans, this has worked well for us. Likely due to the fact that neither of us "lost" the kids or has been painted as the "bad" guy.
I think the comments by feministwarrior have merit. You husband is immature & selfish. Parenting requires the opposite traits.
From the lies your ex-H told, he is manipulative. His girlfriend sounds even worse, like she might enjoy inflicting pain on others with her head games. She is not anyone you want around your kids. If she gets wind that you don't want her around your kids, she'll want to be around your kids.
Chances are, she won't want to be around your kids... she's in her 20s and is really selfish. Having kids to care for on the weekends/holidays will put a damper on their "relationship." She will complain to him & it will become an issue. Make it easy for your ex-H to go long stretches without seeing the kids, attending school functions, etc. & document it. Make sure the schools have your ex-H's email address so they can send him alerts directly.... he'll blow them off & won't read them. Be cheerful in your interactions with him, it will make it easier on your older daughter & easier for him to "forget" about the kids. If he knows he is not going to get reamed when he returns from a long absence... he will relax into an infrequent visitation schedule that suits him & GF. Let him become deeply involved with his new Life & girlfriend. Let it play out. Document the infrequency of his contact. Dig-up whatever dirt you can on the poor judgement of your ex-H and the GF. Hopefully this will go on for years. Then when he moves to have more contact, you'll be armed to say this isn't the best for the kids. This is really sad stuff.
I sense you are the trusting sort. You may need to find a coach to help you steer this situation to get what YOU need for your children & self.
I wish you well.