Newlyweds with a kid? Yes… the son is her husband's child from before. The guy's a divorcee, in other words.
Literal
Newlyweds is-[despite-なのに] child? Yes... son [topic-は] father [gen-の] bring-child. He [topic-は] cross-one [quotative-という] [meaning-わけだ].
新婚 ('newlywed') is the compact Sino-Japanese noun. なのに chains a noun/な-adjective to 'despite.' 連れ子 ('stepchild brought from a previous relationship') is a compact compound. バツイチ is a slang term for 'divorced once' — バツ is the mark × (used in Japan for 'wrong' or 'struck off'), and イチ is 'one.' The idea is that when a person gets divorced, a × mark is added to their family register (戸籍). バツ二 would be 'divorced twice,' etc. ~というわけだ is the 'so that means' conclusive explanation.