This depends, and I'm going to echo some of the earlier posters.
1. Are you underwater? If you bought in 2010 and a short sale, I'm not sure how this is possible, unless the market dropped even more. (2010/ 2011 was kind of the bottom of our local market). Do you not have at least 5-6% over what you paid for it?
Or do you mean that after you sell the house, you wouldn't have enough of a down payment for the next house? Because that's a little different.
2. How much money are we talking? Example: we are in a crappy school district. Did not have kids when we bought the house. A similar house in a better school district was $150,000 more. Private school is about $13-15k per year. So, that's 10 years of private school. Elementary school is only 7 years. Cheaper to buy the cheaper house and do private school if you only have one child.
3. Define "bad school district"? I am in So Cal. The only real way I'm able to judge school district is by test scores - hey, it's a number. So to give you a sample of our local elementary schools:
School A: top school, scores a 10/10 in school rankings. Predominantly white and English origin speakers, <20% of students on free lunch. GATE magnet program there. All of these factor into their "superior" test scores, plus their wealthy parents raise $250k per year for extras.
Schools B and C: close to school A in demographics, score around an 8 or 9 out of 10.
School D: half Caucasian. Half Latino. About 40% English learner, about 40% on free lunches. These categories sometimes overlap. Scores a 6/10
School E: 20% Caucasian, 80% Latino. 60% English learner. 70% on free lunch. 50% bussed from the city. Scores a 3 or 4/10
Schools F, G, H, I: >95% Latino, 85% English learner, 95% on Free lunch, so all students get free lunch. Scores a 1 or 2/10
School J: magnet transfer school, traditional, wears uniforms, year round school, mostly Latino. Scores a 4 or 5/10
School K: magnet transfer school, fluffy, loosey, not terribly academically rigorous alternative school, mostly White. Scores a 3 or 4/10
Now, you cannot really compare the test scores fairly at all. Test scores tend to follow money and language. You cannot "fairly" say that school A is awesome, because they have the GATE program, so GATE students from ALL schools transfer there.
If there is a reasonable number of students in the various categories, they break it down by group. That's where you get useful info.
Now, I live in CA. No child left behind means open transfers allowed. But there's never actually room for transfers. Unless you want to go to the fluffy school K.
School A has room for about 15 transfer students per year. Priority for transfers goes to children of teachers, siblings of students already there, English learners attending a bad school, etc. etc., ending with "everyone middle class". This school is hit or miss. I know many families whose elder children went there, but no room for the younger.
School C doesn't even have room for the students in their district, so many of their students have to go elsewhere.
Anyway, we are in district of, let's say, G. We attended this school for preschool. We opted to transfer for kinder. Because honestly, I wasn't sure I wanted my kid to be one of 7 white kids in the whole school. Our friends kept their daughters there. And tried to convince everyone to stay (30 families transferred out). They eventually left, as did the other family down the street. It's hard to attend a school where most kids speak Spanish, and where they cannot communicate and the education is not geared toward them.
We transferred to school E. Huge educational challenges in our school. How to teach to the English Origin kids (which apparently is pretty easy, because our "English Origin" test scores are as high as every other school in the district, including School A. This, my friends, is why I looked at the details and the demographics before we transferred.) How to teach the English Learners, who are often poor, bussed in, live in multi-family apartments, don't own books, have parents who don't speak English, etc. Our school, honestly, fails at this. There is only one school is the district whose test scores for this demographic are worse than ours.
And then there's the money issue, as district / state funding does not cover art, music, PE, computers, or science. It's very hard to raise enough money to provide these for the school, so we just shrug and figure we'll do our best.
So, how bad is the school, really? Unsafe? No kids like yours? Because in the next town over, I have friends who make disparaging comments about their own school districts, and their overall scores are WELL above the school that we TRANSFERRED INTO.
My son is thriving in school E, where he's definitely a minority, and many students are poor, on free lunch, etc.