I was in a once a week R for years with Josh due to our locations and it worked out fine. But it was what we both wanted. Neither of us was clingy or needy and we filled the rest of our week with family, hobbies, work etc. We did commit to talking on the phone 2 or 3 nights a week when we were not together. But that was just us.
Her reactions and willingness to take whatever struck me funny too. I second what Wii and GMom said.
Your thought patterns seem to be a bit scattered here about what you want and what you're ready for. You need to get really clear about what you want.
And best to get all your financial stuff sorted before you get too involved with someone else. Dating can be expensive. I last recall that you took your daughters to a night in a hotel but you were also still selling blood? Ummm - I can't make sense of that.