This question isn't really answerable, or even amenable to much guidance, on the information supplied.
I'm going to urge you to take a huge step back and answer some much bigger life-philosophy questions first. Once that stuff is aired out you might be able to arrive at a more useful answer to your stated question.
Let me start with an observation: With a $2 million net worth, you are already -- almost certainly -- financially independent. My rule of thumb for the financial independence of a family of four is $1 million invested (that figure's a couple years old and could probably stand to be bumped to $1.1 million, but I'm too lazy to look up the CPI data) plus a paid-off house. That's $40,000 per year spending money purely from passive income (see: 4% safe withdrawal rate) without having to worry about the rent -- I'm generally in favor of minimizing fixed expenses when living purely off investments because it helps people sleep better while the investment markets zig and zag. The underlying logic to this rule of thumb is that the median U.S. household income is around $60,000 per year, so $40,000 in spending money plus a rent-free house is economically equivalent to that, roughly speaking. Showing a lower headline income on the family tax return is usually a big advantage in terms of tax rates, Obamacare subsidies, etc., in addition to the "sleep at night" point.
You easily exceed this threshold. By a lot. In at least 9 out of 10 of cities and towns across America, you can get far more house than anybody should even really desire for $500,000, leaving you with at least $1.5 million invested, or $60,000 per year spending money, and no rent or mortgage to pay. That standard of living probably puts you ahead of 70% or 75% of the entire country, entirely on passive income.
Congratulations, you've won the game of money!
So before charging ahead into extra innings, you really need to put some bigger picture things on the table: What are your goals? Why are you continuing to work at your chosen profession (whatever it is); why are you continuing to save; and why are you continuing to live in your neighborhood?
I don't mean these questions facetiously, or with the intent to pre-judge. The answer to some of these questions may be "inertia" -- we all fall prey to that -- or the answers may be part of a well-thought-out-plan, or they may be part of a plan you adopted by rote some time ago without really deliberately weighing the alternatives, or at least without having recently reviewed them.
Put another way: if you took this cash-out refi, invested the money in securities and did well over the next eight years leaving you with $250,000 more than you would have had in your pocket had you not bothered with all this, what is your plan for those incremental dollars? What would you put them towards, in terms of obtaining goods, services, status, financial security, the ability to make charitable gifts, or whatever? You need to start answering this question before anyone can give you meaningful advice as to whether you should lever up to invest more (higher-risk / higher-reward strategy) or whether to restrain your balance sheet and leverage. But there is one thing I can tell you: the answer to this question cannot credibly be that you need an extra $250,000 invested in order to have reasonable assurance that you can meet your basic needs for food, shelter, clothing and physical security while living in the U.S.A., on the passive income generated by your assets. Because you've already got enough assets for that by a huge margin.
Personal finance is equal parts personal and financial. Your personal goals come first whether you know it or not; the financial strategies follow.
