Let’s get two little things out of the way first. You don’t write or say levar-os: levar + os becomes levá-los. And you don’t write a onde separately: you write aonde. Now the important thing: you need onde in both sentences: so your choice really is between até and a (and a merges with onde to form a single word):
(a) Eu me dirijo até onde os meus filhos moram para levá-los ao parque.
(b) Eu me dirijo aonde os meus filhos moram para levá-los ao parque.
Now both sentences are correct, meaning “I go to where my children live to take them to the park.” But they are not particularly idiomatic. From now on bear in mind that I’m from Portugal, and what sounds more idiomatic to me may not always sound more idiomatic to a Brazilian.
If I had to choose one of the two sentences I’d go for (b) because me dirijo até sounds particularly odd to me; me dirijo a is a lot more idiomatic (in Google Books me dirijo a/à/ao beats me dirijo até 85 to 1).
But even me dirijo a (some place) may not be what you’re looking for. Dirijo is present indicative, and, as with most verbs, you do not usually use the present indicative of dirigir to refer to what you’re doing right now; you can use it instead of the pretérito perfeito to tell a story of something that has already happened. So your sentence actually sounds like part of a larger story, as in the following examples (modern spelling; my emphasis):
Ao receber essa comunicação, dirijo-me à casa do juiz de paz […] mas sua senhora, assegurando-me estar ele mal de saúde, não me permitiu que com ele falasse. Dirijo-me à casa do tenente-coronel Joaquim Francisco Gomes de Castro, e o convenço da necessidade de acabar […] [Anais do parlamento Brasileiro, 1861] [As I receive that communication, I set off/go to the house of the justice of the peace […] but his wife, assuring me of his ill health, did not allow me to talk to him. I go to the house of lieutenant-colonel Joaquim Francisco Gomes de Castro, and convince him of the need to finish […]]
Na cidade de Machu-Picchu ― Digo adeus a Cusco, e, às dez da manhã, dirijo-me à estação de caminhos de ferro. A carruagem é banal, mas correta. [Maria Assunção Avillez, Viagens, Almas e Vidas, 2004.] [In the city of Machu-Picchu ― I say good bye to Cusco, and, at 10 am, go to the railway station. The coach is ordinary but decent.]
To tell someone what you’re doing right now, you can say estou me dirigindo or you can use vou. Unlike most verbs we use the verb ir to describe what you’re doing right now or are about to do.
In your context vou a and vou até work equally well. Generally I’d say in this context vou até suggests you can take your time to get to your children’s, and once you get there you can hang around for a while before taking them to the park. Vou a is neutral: it suggests neither that you can take your time nor that you’re in a hurry (but is compatible with both). Vou até sounds particularly natural in situations like these:
Estou farto de estar em casa: vou até ao café. [I'm fed up of staying at home: I'm going to the café.]
Apetece-me passear um bocado: vou até à baixa. [I feel like walking around a bit: I'm going to downtown.]
Note that in these sentences you could also say vou ao café, vou à baixa. (In Brazilian Portuguese you can say até ao café or até o café; in European Portuguese, only até ao café; same thing with até à/até a.) Até also sounds particularly natural if you mean ‘up to (but not beyond)’, in which case it does not matter whether you can take your time or not:
Todos os dias faço uma grande caminhada: vou até ao fim da praia e depois volto pela mata. [I go for a long walk everyday: I go to end of the beach, and then come back though the woods.]
Vou contigo até à Praça da República, mas aí tu viras à esquerda e eu tenho que virar à direita. [I'll go with you as far as Republic Square, but there you turn left, and I have to turn right.]
On a final note about your sentences, even vou até onde/aonde moram os meus filhos doesn’t sound particularly idiomatic. Wouldn't vou a/até casa dos meus filhos suit your purposes? It sounds a lot better.