Congratulations, being a first time Dad is amazing. I was in your shoes two years ago, and will be again in 25 days (ish). What I learned is my sport took a back seat. It is still important to keep fit, but focusing on training should take a break for probably 1 year. I continued to work out in the morning while everybody slept, and took my son on runs while he napped. I found my wife quickly developed hard feelings towards my sport, only because I was new to fatherhood and did not realize what needed to change. Turns out everything changes:)
Not to say it is not possible…I work 50 hours per week, train only about 10 on a high week, manage lots of family time and still make it to church (occasionally) and put in community hours. My tip is, put training behind you for at least 6 months to 1 year. Keep fit but don’t train like a mad man. These are precious days with your little one, enjoy them.
Triathlon will always be there, your kids wont be.