Now that the whole class has had a try and even David, who says that it is his mother tongue but whose other answers are all in English, made mistakes using "my" instead of "our", leaving a preposition out and using the wrong tense, here is the French Teacher' s version.
I take it that your cousin is British and has married a French girl. This is what would be written in France, but you could cut the "Nous vous envoyons" out and start with "Nos meilleurs voeux..."
Chers Darren et Céline,
Nous vous envoyons nos meilleurs voeux à l'occasion de la naissance de votre bébé et nos félicitations à Lilie d'être devenue une grande soeur.
Avec toute notre affection,
French people do not finish their letters with "Tout notre amour", it is an English colloquialism . "Avec tout mon amour " is what a lover would write.
"La soeur cadette" means younger sister. The elder sister is "la soeur ainée". We do say " grande soeur", and it is exactly right for this context.
As for "formation", which means "training": those on line machine translators do come up with the oddest of things.