First, a few words about retirement accounts:
Set up automatic 401k contributions and max it out if you're not doing so already (it sounds like you're not). At your income level, your marginal income tax rate is 18.46% (federal + state), so if you're been leaving $10,000 of contribution space unused in your current budget plan, you are voluntarily paying $1,846 more in taxes each year, needlessly. Don't do that.
I will assume that your wife does not have access to a 401k plan while she's finishing her masters, but you can open an IRA in her name instead. I'd suggest opening Roth IRAs for each of you and contribute the maximum to each ($5,500 per person per year) instead of converting the existing 401ks. You should have $25,000 or so left in cash after buying the house, so just write out an $11,000 check to Vanguard and call it a day. You can contribute in the name of tax year 2017 until April 2018, so you have a few months to figure this out. Bonus: Principal contributions to a fresh Roth IRA may be withdrawn without tax or penalty, in case something comes up later and you realize you need some of that money back. A Roth IRA containing 401k conversions, however, is subject to a 5 year seasoning period before you can pull out cash. Don't bother trying to convert the 401k money into Roth IRAs at this point.
The reason for this is tax diversification. There will come a point, starting at age 59.5, when you can withdraw from a 401k but avoid taking social security (which is good, because the later you wait to take social security, the higher your monthly check for the rest of your life, which is a very cheap and easy way of giving yourself some insurance against outliving your private savings). Now, a regular 401k withdrawal is treated as taxable income, but the trick to taxable income is that the first $20,000 or so per year per married couple is essentially tax free (adding up your standard deduction and personal exemptions), and the next $18,000 or so is taxed at 10% federal (and at a lower state rate than you pay now). That means you could have $350,000+ in a regular 401k starting at age 59.5, be early retired at that point like a good follower of the blog (meaning no other wage income), and pull all that cash out over the following 10 years while paying vastly lower tax rates than you do now. If you convert now (or fail to max out your 401k now), a big chunk of your nest egg disappears to taxes permanently and early, and you lose the chance for that money to compound and grow to your benefit. Now, tax rates do change from time to time, and neither of us can predict the future with certainty, but the standard deduction and personal exemption are pretty long-lasting aspects of American tax law, so it seems very highly likely that there will be some opportunity under the tax code to pull zero-tax income out of your 401k when the time comes. My view is that you have to expect your 401ks to hit $250,000 in value before even thinking about Roth conversions, with the exception that if you have a year with extremely low income, giving you the opportunity to convert at a tax cost of zero, it's obviously worth taking.
Normally, in this space, I also advise families who are trying for children to start 529 college savings accounts right away and take advantage of any state tax deductions -- name a parent as the beneficiary until you have a kid, and then simply switch the designation. In theory that's right, but given your current income level, state tax rate, and other priorities, the benefit is probably no more than $70 a year, so I wouldn't stress over it. Maybe next year, if the family income is substantially higher. Focus on the 401ks and IRAs for now, which is probably all you really have capacity to fund at the moment.
Second: You need to track expenses better, which other people have pointed out. For starters, you have no monthly line items for irregular automobile expenses such as car insurance, repairs, maintenance and depreciation / replacement reserve. Given your fleet and your gas bill, I'm going to estimate those aggregate to $250 or $300 per month average, if you costed it out properly. Similarly, nothing for clothing or medical expenses (is the $5,000 per month income before or after your contribution to your health plan premium? what about co-pays and out-of-pocket contributions for doctor visits and prescriptions?). No travel or vacation budget? By the time you're done adding all this up, I bet your average monthly spend is much closer to $2,800 or $3,000 than the reported $2,200.
Third: Your automotive fleet is excessive. The '04 Corolla is probably worth around $4,000. The '13 CRV is probably worth close to $18,000. That totals to roughly 15% of your net worth, or a third of your yearly family income. You've said nothing about your travel and commuting patterns, but at a minimum the $18,000 CRV could be replaced with an $8,000 used Honda Civic or Fit, freeing up $10,000 which you could invest or use to pay for your home renovations without side-tracking your automatic savings plans. If you were more aggressive with your lifestyle, it might be possible to go down to a 1 car family, and replace the second car with an electric bicycle or a Vespa-type scooter, which would free up $17,000 of capital and put a good $100+ dent in your monthly ongoing car-related expenses.
Fourth: Starting a family. This is probably the most important thing. If you want kids, have them sooner rather than later. It doesn't get easier to stay up all night looking after a puking baby when you get older! At the same time, you are in a big transition year in your family's finances and earnings trajectory -- your changing careers, your wife finishing up a masters with the potential for higher earnings in the near future, and your buying a new house. It probably makes sense to wait just a little longer in your case, but I strongly caution against waiting too long: about 2 more years, max, until you start trying is my best guess. But kids are the meaning of life and all that, and if you were hoping for a larger family (4 or more kids) frankly you're better off starting THIS MINUTE and sorting out the finances later. Have an honest conversation with your doctor: fertility problems increase a bit after the mother hits age 30, and a whole lot after she hits age 35. (The age of the father is a much smaller factor.) Don't miss the boat here.
In conclusion: Don't take the above suggestions the wrong way. Your basic habits and instincts seem very good -- decent family income, paid-off cars, no debt except for a reasonable mortgage, a good start on retirement savings, and fundamentally reasonable spending habits based on the big categories you've reported so far (housing costs, food budget, type of car you drive). I think a few of your questions have some pretty clear answers, and there are a few clear points for optimization, but my feeling is you are far from the sort of "HAIR ON FIRE!!!!!" emergency that the blog author loves to speak about with lots of exclamation points. Assuming your family income goes back up a fair bit once your wife finishes her masters, you could find yourself at $100,000 invested net worth, plus $40,000+ in home equity, in just a couple of years. Things will probably slow down a bit once you have children, but if you are in the market for a long-range goal, I'd suggest having $500,000 invested plus a paid-off house to live in by age 40. That will give your family massive flexibility when it comes to work, lifestyle, child-rearing and pursuing outside interests. In those circumstances, one parent could work a half-time job and have more than enough income to sustain the family in the greatest comfort.
Congratulations on the new home, and good luck!