I met my second husband 8 years ago. I had 2 young kids, he did not have any. We only saw each other every other weekend, maybe a few weekday nights, it was hard because we BOTH wanted to see each other so bad. I too did not want him to meet my kids because the relationship was new. After 6 months, he told me he "wanted to meet my kids as soon as possible, and could it be this weekend"? I will never forget that, he truly wanted to meet my children, we BOTH had fallen in love, but we took our time (I was newly divorced).
If she really wants to spend time with you, she will make time. If 2 people really want to be together, they BOTH make it work. I would get closure with her.