-Thank you for your question. I will reply in two points, one (a) theoretical, and the other (b) practical.
A. First, to the theoretical side of it. Why avoid the Novus Ordo Mass, if it is valid?
Indeed, the Novus Ordo Mass is, in principle, valid. But "valid" is simply a technical term which we say of Masses which are true Masses. If a Mass is "valid," that just means that it is objectively a true Mass, with a true consecration and sacrificial offering of the Body and Blood of Our Lord. It does NOT mean that everything that the priest and/or people do, think, mean, etc. is pleasing to God or even conducive to salvation.
To put it in theological terms, "valid" means that "ex opere operato," by virtue of the (objective) act itself, the Body and Blood of Our Lord is truly made present and is offered by Christ the High Priest to the Eternal Father. But that says nothing of what occurs "ex opere operantis," by virtue of the work of him who works (i.e., subjectively). So a valid Mass could still be sacrilegious.
Now, I would argue that the Novus Ordo Mass, as it is usually done, is sacrilegious and harmful to the faith. (I mean this about the way it is actually said, NOT about the way it SHOULD be said---everyone facing east, in Latin, with the Roman Canon, with the best "options," with Gregorian Chant.) Let me explain: the average Novus Ordo parish simply presents the Holy Sacrifice of the Mass as not being a sacrifice at all; as being merely assembly which celebrates the fact that it is together in community. It treats the Body and Blood of our Saviour as a mere symbol of unity and love. It turns all external acts of divine worship into an anthropocentric activity. This watering-down of the Mystery of Faith is offensive to those who know that the reason we go to Mass is to participate in the sacrifice that Christ, through the priest, offers to the Eternal Father as the supreme act of divine worship.
You simply cannot pray when everything around you is a blatant attack of the faith in the true nature of the Mass. We are physical beings and we need external signs in worship to lead our minds toward the interior realities that they represent. And if this is true of adults, it is all the more so with children. It would simply be scandalous to them, and their simple minds would be corrupted. They would see little reverence for the Blessed Sacrament; they would be confused about their faith; they would become unconnected with the tradition of the Church; they would lose almost all sense of the beauty of the liturgy; etc.
So, in sum, "ex opere operato" the Novus Ordo Mass does the job (i.e., it is valid). But "ex opere operantis" it is destructive of the faith. So that is why I try to avoid the Novus Ordo (at least the average Novus Ordo) as much as possible. The Church would never force us to do anything that is harmful to our faith anyway.
Therefore, I would have no scrupules in attending (or taking my children to) an SSPX chapel for Mass if that is the only Mass available that is not offensive to the faith. Rome herself has openly allowed this, provided it is not done "in a spirit of schism." However, I would beware of becoming formally involved with the SSPX until they are regularized (if it ever happens).
For a faithfully-orthodox summary of the problems of the New Mass entirely devoid of any "spirit of schism," see the classic by Carinal Ottaviani (former head of the Holy Office), A Short Critical Study on the New Order of Mass (aka, The Ottaviani Intervention).
B. Now to the practical problem. What should you do? I would first look for the following, in this exact order:
1) An episcopally-approved traditional Mass. If I have no luck, then:
2) A Byzantine (or Eastern-rite) parish. If still no luck, then:
3) An SSPX chapel.
I myself have never attended an SSPX Mass because I have never been in a situation when only (3) has been available to me. There always seems to be either (1) or (2), or both, available.
Looking at the Directory of Episcopally-Approved Traditional Latin Masses and the The Unofficial Directory of Eastern Catholic Churches, it looks like you might have a few options in LA other than the SSPX chapel.
Note, however, that when you attend a Byzantine Divine Liturgy (i.e., Mass) for the first time, you're in for a big "liturgical culture shock" (in the good sense). The Divine Liturgy is very different and yet very similar to the traditional Mass; it is spiritually edifying and very educational to attend there occasionally, and it could be a life-saver (or "soul-saver") when there are no traditional Masses available.