To answer your question, it depends on whether Kaine had a will in place. If he did, it probably divides his estate equally between Terri, Kyron, and baby. Or perhaps between Terri and Kyron, expecting Terri would use her proceeds to care for the baby. If there was no will, I believe the Oregon default when there are children from a previous marriage is half to the children from the other marriage, and half to the current spouse.
Either way, Kyron would be receiving a large chunk of the estate, whatever that might be, regardless of his age. If he were still a minor, it would be put in a trust for him until he comes of age. Since Terri is not on the mortgage, she would not automatically inherit the house free and clear. A portion would be Kyron's. Same with retirement funds, life insurance, and any other money.
Desiree, as the next of kin to Kyron, would take custody of him, and his inheritance trust. It is quite possible the house would have to be sold.