Are marriages not concluded in Church valid in the eyes of the Vatican? Will the resulting children be baptised?
If only one of the two partners is Catholic, the marriage has to be solemnised in a Catholic church, otherwise it is not valid (cf. Can. 1117).
If the marriage is not valid, the children cannot at first be baptised. There will be a postponement of baptism (cf. can 868 § 1 n. 2), until it has been ascertained that someone (relatives, godparents etc) can take on the Catholic education of the child.