Again, welcome to the forum.
I'm going to give you a link to the USCCB (US Conference of Catholic Bishops) site - specifically to An Agreed Statement on Mixed Marriages
. This is a product of the North American Orthodox-Catholic Theological Consultation. It's old, issued in 1971, one of the very first documents ever produced by the dialogue, yet it still reflects the joint agreement between the participant bodies to the dialogue.
Nothing in it will resolve either of your concerns - which turn on events that would transpire after the phase addressed here, but I thought it worthwhile to offer the background that the dialogue would have suggested.
As regards the marriage having been celebrated in an EC, rather than an EO, temple, you ask
what the Orthodox person must do to be able to get back into good standing with The Church?
And, as regards the children having been baptized and chrismated in that same EC temple, again with respect to the Orthodox spouse's standing iin his or her Church, you ask
how would this situation be resolved?
As my brother, Bob, said, both questions need to be addressed to a priest of the Chuch from which the Orthodox spouse originated (presumably, the same with which she or he seeks to reconcile - if not the same, to a priest of the Church with which reconciliation is sought). You are correct in your supposition that the children cannot be re-baptized or re-chrismated and I doubt that a repentant lapsed Orthodox spouse would be barred from the Mysteries until the children reach majority and choose between Churches. One would hope that charity and economy would not countenance such a result.
The answers to your questions, may indeed vary depending on the particulars of the Church and even the jurisdiction involved (and, although they shouldn't, perhaps on personalities). One should be able to say that the answers are X and Y and that there would be consistency across the board, but too many years witnessing too many variations make one leery of supposing that to be the case.