Congratulations on the addition to the family.
THE most important thing is going to be your diet, sorry to say. You're not going to be able to make any marked process on workouts alone.
There's programs out there that will tell you exactly what to eat. The basics are meat: chicken, eggs, lean beef, fish and vegetables: spinach, beans, tomatoes, brocolli, etc. Very little starches and processed carbs, potatoes, bread, etc. Don't be afraid of good fats like olive oil and nuts, have multiple servings a day.
On the workouts, again there are a ton of programs out there. I'd focus on resistance training the whole body given your time constraints. Complex movements like lunges, squats, deadlifts, cleans, etc. You'll be better served doing these exercises at a quick pace, with little rest, that running on the hamster wheel.