I’ve found the whole ivrit thing very difficult l’ma’aseh. On the one hand it’s really disgusting to hear the things people say on the street in modern hebrew and how our holy tongue has been perverted, especially when you hear vulgar people speaking. I read in a biography of Reb Yoilish that he once said, “I wish I knew hilchos Shabbos as well as I know that it’s assur to speak ivrit!”
On the other hand, as a baal teshuva with absolutely no Jewish schooling growing up (not even reform) the difference in my learning ability before I went to ulpan and after was basically in different galaxies. So on an idealistic level I’d like to poo-pah ivrit but on a pragmatic level without my knowledge of ivrit my kodesh learning would be limited to very little beyond English translations.
Also we send our kids to chinuch atzmai schools so anyway they are learning in ivrit (albeit peppered with a lot more lashon hakodesh and yiddish than ivrit on the street). We toyed with the idea sending to yiddish speaking only chedarim but it’s just too big a leap for us.
With regards to the OP – regardless of your stance on lashon hakodesh vs ivrit, (and with all other things being equal as far as your ability to do so) the easiest solution would be to make aliyah so that your children grow up learning Torah in it’s natural language to begin with!