Of course it's not either/or.
But she has to ask herself if her H is likely to drain any joint current or savings accounts while she goes through the process of the religious divorce. He has been revealed to be a liar, an adulterer, a bad husband over the years even before all of this came out, and he has gone against the protocols of Islam to boot in engaging in the second relationship. He has brought several children into this sorry and sordid mess he has created and seems to value the OW only for her sexual services. He seems quite openly hostile toward the OP, completely unwilling to admit any wrong, and in fact exhibiting an attitude of arrogance and entitlement, and he refuses to to apologise or assure the OP that he holds her in any sort of regard. What she has reported of his remarks is basically, "Me, me, me, me, me, me, me. Me and my prerogative, my sexual satisfaction, and you can like it or lump it."
I wouldn't put it past this man to steal money from the OP and from her children or to leave them penniless and even homeless. He sounds like a nasty piece of work and from what she says he has been nasty for a long time.
So she can waste time and energy securing the religious divorce when she really, really should be pursuing whatever legal/civil rights she has. It doesn't have to be either/or, but she needs to prioritise and her priority should be her legal rights and the rights of her children to financial support and to keeping their own roof over their heads.