dividing a lot with a mortgage, finance question

[Bryan Pope]

So basically I'm dividing a lot into 3 lots, and building a house on one of them right now. There was a miscommunication between the civil engineer, builder and city, and originally they were going to let me build the house before partitioning the lot but now they're making me do it now. Construction costs have also gone over a bit and I'm going to need to get some money to pay the builder once he's done. 

it's kinda messed up that the city approved plans and then later tells me I need to partition the lots, is that normal?

Is it possible to refinance the new construction even though the current mortgage has interest in it? or would a heloc be the best route to go? I won't have enough equity in the the first house to finance anything and I don't want to give up my 3% loan, so I need the equity in the new construction to qualify. But if the current mortgage has interest in it, would I not be able to take another mortgage out on the new construction without a partial release of interest? seems like they won't do that because I don't have enough equity in the first house. 

What's the solution?