I too am involved with a fundraising and awareness group. There is a similar organisation with slightly different aims in our city. After a couple of 'difficult' situations we now have a sit down at the beginning of the year and share our calenders so that there are no clashes. Our group made the first overtures, with the theme of making the most of public exposure to our cause. It has worked well and now we make sure that there is a happening once a month with both groups taking turn at events. Occasionally we have events together and sometimes we have extra events that get added throughout the year, but never on the same day as a happening for the other group.
As the chair of the fundraising committee, I make sure that requests for assistance are written and on headed paper/email so that the contributor understands which group is asking. These letters also set out what each of us is providing in the way of paying for ingredients etc. That makes thank you notes in the programme very easy.
Fund raising is hard enough as it is without the complications Babymama has encountered.