It's not that easy (or cheap!) with children.....
I agree with everything that's been said so far. I moved to Sosua from UK in Aug 2006. This is my overview of things where I am as a fairly new resident and one who has young children (2 and 5):-
I live near the International School in Sosua (they have website), which is where my two young children attend school . The International School is expensive (approx $500 per month per child with meals). There are other cheaper private schools nearby (Learning Centre was $263 per month, Garden Kids (they have website) is prob cheapest - both good education). Also there is the Louis Hess School in Sosua and the Nueva Vida School near the International School if you're children speak fluent Spanish (I believe the Hess school is better.......). I'm not sure about facilities for children with learning difficulties.
I moved here with my partner (although it feels like I moved here on my own a lot of the time as I never see him!), but financed everything myself. He works as a dive instructor. The MOST he can earn in Sosua is approx $1000 per month (inc commission), but he can earn four times that if he works away on the liveaboard boats for 10 weeks at a time! Wages here are very low, so don't bank on keeping a family purely on your income, if that's what you're looking to do. I've kept a close track on finances since we moved here and we need approx $2500 per month to live on inc school fees., and that's with our house paid for cash! I've spoken to a couple of other parents and they agree with me that approx $30,000 per year is minimum. That's not for an extravagant lifestyle. It includes maintenance (water, security, rubbish collection), electric (expensive here), petrol (going up all the time!), medical expenses, eating out once or maybe twice a week, sensible shopping using mainly local produce, kids activities (karate, horseriding, ballet - there's something going on every night at school etc and it's difficult to say no when all the other kids do it! Same as anywhere else!). Shopping bill here is similar to UK (some things cheaper, some things more expensive but it balances out). I feel like I'm paying out constantly. Perhaps it's because you have to physically pay everything in cash......but even long term residents agree with me that the 'paying out' here seems endless. I don't know why you're leaving Spain but don't do it because you think it's going to be more economical. Also, relocation expenses, flights, shipping, purchasing new items here (like a car, essential really if you have two children) and settling in means that your first few months will be much more expensive.
Lastly, if I'm to be truthful, I miss many more things here than I ever thought I would. Living in Europe you're in close proximity to lots of cultural destinations, you can get English books and items delivered easily, you have access to very good medical facilities etc. I love the fact that my children have an 'outdoor' life and they enjoy it, but it frustrates me that I can't take my 5yr old to the theatre, the ballet, or a museum or just easily go and buy her a book or film or dress we've seen advertised. It might sound shallow, but I've grown up in a consumer society and I enjoy shopping.....
You could live in Barcelona or Madrid, or you could live on the Costa del Sol as you don't specify. I've just given you some thoughts as I'm not enjoying it here as much as I thought I would, despite the fact that I've met some lovely people. I do understand why people love it here, but with children it's a whole different ballgame.....
My big reason for moving here was to be near my children's' only surviving grandparents, and I thought it would be good for them to be near some family, but it transpired that the 'grandparents' (despite false promises to get us here!) weren't actually interested in spending any time at all with their grandchildren and that my friends in UK were more family to my girls than these people ever could be!
Anyway, the reasons you're moving here are as important as anything else. Please say it's not a man! You need to think long and hard as the Dominican Republic is not Spain, even though they share the same language. If you're determined to try it, then just rent here and put your things in storage.