The thing is the op is not looking at it from the companies perspective. The op says this woman came in with contacts, she says she managed to start talking to the funding body, indicating the op never managed this, and as such it made sense for her to do it.
start ups are notorious for failure, sustainability is becoming a crowded market in terms of start ups. They need to do what’s best for the business to drive it to success. Giving the project to the op would not be best for the business, just best for the op. Why wasn’t the op able to speak to the funding body, she had way, way more time to make connections and try than the other woman.
the use of the term collaborative here is simply the op wants to share the project with her, this isn’t a hobby, you don’t share, you do the job allocated, as the company wishes. Not job share out of kindness.
amd the woman didn’t appear out th4 blue as she lost a job. She didn’t just turn up on the doorstep. The owners clearly undertook a conversation and interviews and decided to employ her for the 3 days a week. The woman is clearly trying to build that up further and do the job awarded to her. Asking her to job share is simply embarrassing and unrealistic.
the op needs to be more proactive. Not ask them to force her to share. Not ask them what her role is. But think about where she can add value. She works one day a week. She need to think about how she can add value, grow the business. Put a proposition forward, and then also see her doing, understanding she’s employed only 1 day a week. Not say well I’ve been here two years for a day a week so I deserve it more.