A loan modification is generally allowed by a lender because you are having financial hardship that you documented to them. Usually, your credit has already suffered a lot because of those difficulties.
Despite the fact that you have received some assistance from your current lender on a mortgage that is probably around the same level (if not lower) than a new mortgage on the foreclosure you're considering, you should stop and count your lucky stars.
Financial difficulties often come from life circumstances that we're just not prepared to handle, like a layoff or medical bills, but those are supposed to teach is to prepare for future problems.
It sounds like you were over-stretched or at least didn't have a plan that covered difficulties before. It would not be prudent to step into another situation with the same or higher mortgage payments without first considering your financial plans.
Take a moment and think about what you would do if the same events occurred on the new house. Would you have the same set of problems and ask the lender to modify your loan? If so, it's time to get organized and sock away some reserves and build your finances and change your spending habits to provide a way out for your family in case of difficulties. Do this before looking for another house.
All of us want to have a nice place to live with plenty of space, but temptation surrounds us on every turn, not just a bigger better house but flat-screen TVs, new cars and so on. We have to learn to cope with the hand life has dealt us. Lenders believe this also, which is why they demand that you demonstrate you have learned your lesson by not having lates or collections for 2 years after you get away with a short sale.
Take stock of what you have financially and spiritually, and try to be happy. Temptation is the road to destruction.