Hi Matt,
Just ran some quick, simplistic numbers. Spreadsheet attached - it looks to me like you can make the move within your month-to-month budget - assuming you're OK taking on a lot more debt. You need to evaluate that against your goals, FI and otherwise. If you want to get to FI quicker, look for a cheaper house or stay where you are (obviously).
The way I figure it, on a pure monthly cash flow basis you either pay $125 / mo additional to live there or, if you factor in your saved commute time valued at $25 / hr per person, you actually save $376 per month.
What this doesn't take into consideration is the additional interest you'll pay. If you were to refi your existing $107K at 3.5%, 30 years, you'd pay $65,972 in interest over the life of the loan. For your hypothetical $225K house, it would be $107,898 over the life of the loan - a difference of $41,926 (approx $116 / month) which, if invested at 5% over those same 30 years, would $88,828 additional savings in your 'stash at the end of it all.
Another way to think about the interest is: you'll pay $332,898 over the next 30 years for the privilege of living in your hypothetical 4 bedroom home, vs $172,972 to stay where you are.
FYI, by way of comparison, my wife and I have 2 children and we all share an 1,100 square foot, 3-bedroom 2-bathroom apartment quite comfortably. 2,500 sq ft should be considered a luxury.
Some notes on my spreadsheet assumptions- I assumed you pay 4% now on a $107K loan, and assumed $175K loan at 3.5% in the new property
- I estimated 50 minutes per day commute today, and 20 minutes commute if you move within 10 miles
- I valued your commute time at $25 / hr per person