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Great details. You're in a strong position with great options.
Many guys in here posting "pay off mortgage" but that might be the case for them but that's not the same for everyone. Not that there's anything wrong with that. It depends.
One tipping point number is the ratio of house equity/mortgage to amount of total in retirement:
If your retirement account value is LESS than the equity or mortgage, well you've got a problem and the numbers are too soft. That heads towards slow growth of retirement. Also heads towards, house rich-cash poor scenario.
If your retirement account value is MORE than the equity, that's the position we want to be in. Pay down the house consistently, meanwhile the retirement account builds momentum while the house equity increases at a slower rate.
Remember the goal is the 20 year play. Paid off mortgage, regardless of this house or another, while having $1m-$2m in retirement.
If I was in your shoes, the first thing you are facing is emergency fund then college:
1) I'd top off my emergency fund. Making sure we've got a solid 6 month of expenses(or salary) in the bank
2) Get a more solid investment base for eldest child then figure out how much we will need to cash flow the rest of their college
3) Start a ROTH ira in both the wifes/your names for 2017 and then have the same for 2018. That way you can get that money in the game soon. Your net worth would be growing by $22k immediately after January 1st 2018 then your compounding interest would be growing as well. This is a much better play before buying brokerage account mutual funds outside of retirement.
4) Depending on how much is left, consider child number 2's college, that way it grows over time and you don't have to cash flow it in the future thereby freeing up your income. Depending on the childs age and how much is already in there, you could park $6k-$8k in there for when she's 18.
5) Park the remaining in a brokerage account in growth stock funds with low expenses. That is 20-30 year money and a line item in retirement as well never to be touched.
6) OR instead of 5, consider re'fing to a 15 year fixed if you can keep your note down to 15 years.
That's what I would do.
For my situation, we've got a 15 year fixed with 12 more years to go with only $79k remaining on it. No need to pay more money to it when the mortgage is only about 10% of our take home pay. We could pen stroke a check and pay it off but the money is at play in the market with low risk while making us more money. Meanwhile we are pounding our retirement accounts to the max. The retirement accounts have 2x in them of what the house is alone worth. Everyday our net worth goes up with the different streams of revenue into the retirement accounts while the home equity builds very SLOWLY and contributes to us being set to retire.