I just... I have no idea. I am supposed to be responding to a soft offer this morning but I am not sure what kind of "ball" to play.

Awhile ago my boss took a higher position at a somewhat higher esteemed and larger but hierarchically lower level sister company. My current company basically told me my current position will be dissolved because sister company is going to form a team under former boss to do those duties. I can stay on but would have to take on totally different duties. I love what I do and I think I have a valuable skillset so that doesn't sound appealing to me. I applied for sister company's job and have the soft offer - always being considered a shoe in because - well it's my job.

It's time to negotiate and their offer is OK. I get to keep my accrued leave and my years of service (heck yes!) but the salary bump is a little less than I had hoped for.
Budgets are super duper tight right now and I don't want to push it with new company. Even though I have two options - keep current job or accept new job I feel like I only have one option - go and I don't have any leverage for negotiating. We will not be getting raises for at least two years at either company. I also feel like this will be my only opportunity to negotiate anything for a long time.

If they can't budge on salary should I ask for a sign on bonus? Flex schedule? Or should I just accept the offer (1500 increase from current salary) as is and be done with it?

There is actually more complicated history and stuff but I tried to boil the situation down to what is going on now.

Any advice?