One option would be to use the equity I have in my current house towards the purchase of a second house.

Not exactly, you could use the land as a down payment to pay for construction of a new house on that land; However, to get money out of that land without selling it to buy a house somewhere else, you'd have to take a loan against that land and the bank financing your new mortgage won't like that at all and is not really an option. (This is USA-centric advice)

Edit: for context I went through this process (for my first place I don't own two places) and when you go to get your second home, the first question the bank will ask you is where the money came from for the down payment - if it's from a loan or a gift they will pretty much shut you down right there. A lot of this stems from the '08 crash.