Hello @Lauren Garritano, Congrats on all your success so far. You guys are on an awesome journey.
(1) To get more cash I'd recommend doing a cashout refinancing. You would keep the property, lock in a lower interest rate and get a large sum of cash (tax-free btw). The cash could be used to increase your emergency fund and fund this project. I don't recommend selling anything unless it's causing you problums or doesn't cashflow.
(2) Construction loans for investment properties are becoming more difficult to get. I'd recommend reaching out to local lenders and making sure you get both a preapproval and the loan guidelines before looking to buy land. 100k for a quadplex lot is incredibly cheap, especially in a long-term growth market. I'd work with the builder/agent to confirm the cost of land in an area that would make sense to build in. As you pointed out the downside of going this route is that you are financing the construction. This means that you have the construction loans, end loan, holding cost, paying for all the connection fees, taxes, have to spend the time to figure everything out (can feel like a 2nd job), and close 14 months from now, even if your property doesn't appraise or if we experience a downturn.
(3) Because of the downsides mentioned above, I generally recommend purchasing new construction investing properties from a spec builder. In most cases, the spec builder purchased the lot several years ago and is financing the construction themselves. Generally, all you have to do is review their list of properties currently under development, put 10% in escrow and close on the property once it's completed the same way you would a resale property. We have over 50 properties currently under development in Florida, that we sell directly to investors. At the moment, we don't have any inventory in NC. But there are others that do.
I hope this helps. Let me know if I can provide any additional assistance!