If your husband wears a streimel/chassidish levush your daughter prob will not fit into Bais yaakov. Ik someone who’s father is like this and she’s always embarrassed as most of her classmates fathers are in chinuch... it’s super yeshivish. Some kids in older grades come from chassidish families but now they don’t really accept this crowd. My girls are in bas mikrah and I think that would be a better choice than Bais yaakov. It isn’t chassidish in any way (families don’t speak Yiddish at home) but the girls are more open to other types than Bais yaakov. If u choose a non chassidish school keep in mind that your kids probably won’t be speaking Yiddish at home. Chabad shouldn’t even be an option. I see the kids that go there and definitely not like any above schools. I don’t know anything abt the chassidish schools, but I know that when I grew up Bais dovid and Bais Rochel we’re this type. (Even vein used to be heimish, now they don’t let women drive and it’s reg chassidish). In monsey unfortunately in non chassidish/ yeshivish schools if your husband is working and you try to get into school (after kindergarten/pre1a) they make you commit to paying full tuition. We are heimish background (no chassidish levush) and decided to go litvish bec there were no heimish options
The Bais Yaakov being referred to here is Kesser BY, not Bais Yaakov Elementary that you are referring to.
Kesser BY is definitely heimish/chassidish and instruction is in yiddish. The school was modeled after Bais Rochel of old, albeit a warmer more caring version. Its a great school and a lot of parents who sent older children to Bais rochel and boys to Bais Dovid/Vein now send their girls there.
(I agree BYE wouldnt be a fit for OP. It’s a very yeshivish (as opposed to heimish) school. Streimel wearing fathers are very much in the minority- maybe a small handful in the whole school.)