DUDE - WTAF??? Kids first!
I met my partner 2 years ago and we have almost identical situation to yours. I have no kids and he has 2. His children live about 150 miles away from me - where he is based. He has 50-50 custody.
He is the BEST thing to happen to me and therefore I have uprooted my very mobile, child-free, life (along with cat and dog) to base with him in between my contract work. When I’m working we stay at mine on weekends he doesn’t have kids and his when he does. I have worked very hard on my issues and (very natural) feelings of insecurity to ensure I have a great relationship with his children and he was always clear with me that if i couldn’t handle his children, the relationship would be difficult to make work. I LOVE his devotion to his children.
Your gf is being selfish, insecure and all the issues about you having kids are hers. She shouldn’t have started dating a man with a relationship history if she can’t cope with it. She needs to support you in having the best possible relationship with your children and you need to articulate to her that whilst you can be patient and are there to hear her vent her worries, your children are your NUMBER ONE priority and she must embrace that.
Furthermore, what does it say about the future you’re building together if you can so easily abandon your children? If my partner hadn’t been so clear about laying the boundaries around his kids and had ditched them I wouldn’t have found him attractive at all. His devotion to his children is incredible.
Two weekends a month is sometimes the best that separated parents can hope for, but if you can see them more you MUST. You made them and you have to prioritise them over and above your fear of being alone.
Set better boundaries and get your sh*t together OP. She’s going to try and alienate you from your children and that is a massive RED FLAG. DO BETTER BY YOUR KIDS.