Refinance, home equity or new construction loan?

Hello,

I currently have a 30 year fixed mortgage on my home and owe around $70k. My mortgage payment is $368 a month not including taxes or insurance. I'm 8 years in.

The market value of the home is probably between $250 and $350k. It's an older module, but we've maintained and upgraded. Additionally the house sits on 5 acres and has 300' of river frontage.

I also own 24 acres adjacent to my house property that does not have any lien.

I want to build a second small home on my adjacent property. I'm ballparking around 100k in loan to accomplish this.

I'd like to use my good credit and home equity to get the money I need to finance this project.

Does it make more sense to refinance my existing mortgage to get that money and have a whole new loan with the equity being my existing home, take out a second mortgage against my home or look into a new construction loan? I admittedly know very little about any of this especially the latter new construction idea.

Any thoughts or insight is appreciated.

I think my current mortgage rate is around 3%