I'd go out with Marianne for my birthday as long as you're not likely to run into Barbara. My first instinct on reading what Barbara said is that I can relate. She is a busy Mom with a busy career. I think it is important that she told you what her plans are. But who knows...
I agree that you should be hopeful but stay busy. Find out what will work for her. & when you find that out - you will know more.
Does she know it is your birthday this week? Even if I'd only been out with someone a couple of times - I would send a birthday greeting. I hope she does.