Hi S.,
It is good you are taking everything into consideration well in advance. Short answer: I am somewhat in the same situation as you, and we are staying put.
(very) Long answer from a fellow planner: I think you should stay put. Use your husband's promotion as an opportunity to reserve the extra funds to pay down your debt. I know you would like more space, but think of how much more space your children will enjoy in a few short years when you are able to become a home owner! In the meantime, their ages are still young enough that boy/girl privacy isn't an issue. You can always do things to provide short periods of privacy though. For example, allow your son to have the room to himself for a few hours by taking your younger child to a park or by letting her know that her big bro needs alone time. Make it a game, and it could work.
I really think the larger issue is to consider the cost savings advantage you have to staying put. If you are very strapped for space, then often times rental communities will allow you to transfer within the property or to other properties before your current lease is up with $0 to low transfer fee. Usually your lease will be voided and a new lease will begin, but since you will be a renter for a few years, this shouldn't pose a problem. If you moved, you could bargain with the property for a lengthier lease at a reduced rate. *I've done it, and they do bargain.* Call for rates first, as if you are a new renter. That way you know what they are offering. You would be surprised that with specials it can be less than you are renting at.
As for children switching schools and when is the best time...children are resilient, especially if they have positive support from sources external to the school environment; stable homelife, involvement in other aspects of the community- church, social groups, family close by. However, if you think in the long run you are going to move closer to your husband's work, then I would do it prior to middle school. Middle school age is a time for great change and who wants to be a kid who doesn't know anyone on the first day of middle school?
My husband and I have one child who is of school age. We moved between states three times in our eight year marriage and our child has attended two elementary schools. We currently live in an apartment in Katy. All of the people we know own homes. We relocated here almost a year ago and have decided to stay in our small apartment for several more months. I decided to not compare what we have to families around us. We are younger than most of the families around us and therefore are in a different situation financially. We used this opportunity to pay off all debt and now are adding to the savings we already had while we decide where to buy. In the meantime the housing market is dipping a bit in our favor. It is smart of you to free yourself from debt before making a long-term investment that is going to take up about 40-60% of your budget.
Finally, living close to your husband's place of employment may not be what you want in the long run. What if the schools and neighborhood aren't as good? It is better to do all of your research before you make a move again. Take advantage of this time to do your research. Houston and all of its burbs is a large area with plenty of good and bad neighborhoods and schools. Although my child is only in second year of public school I am researching neighborhoods all the way up to high school and doing 20 yr comparisons on how the areas have or have not changed. My husband works 50 miles (one way) away from where we live and I work 25 miles away. So far we have decided to stay where we are simply because of the schools and the community. When you buy a home you are not only buying a building but you are buying into a community and a lifestyle long term. To get our child involved with other kids (since we do not have a yard or space for friends to come over) we get involved in community and school activities instead.
Best wishes to you!