Translation:Because we are expecting another child, we are looking for a bigger apartment.
Maybe this will answer your question. Since větší is an adjective, it changes its form based on gender, number, and case.
You can find the declension of "větší" here. Click on Declension if the table is not visible. https://en.wiktionary.org/wiki/v%C4%9Bt%C5%A1%C3%AD#Declension.
ČEKAT (without a preposition, and in the context of "having" another child) has been presented in the course as EXPECTING. If we were just "waiting" for another child -- say, another friend of one of our children -- it would be ČEKAT NA.
Disclaimer: I'm learning too, so you may get a more authoritative answer from one of the Czech experts.
It's usually best to keep clauses in the same order, unless doing so would result in a really strange translation. However, as the meanings are the same here, I will add "flipped clause" variants if the Czech natives on team are comfortable with the reversal. It may be something that just wasn't considered when the sentence was developed.
The meaning is the same everywhere. The point is it is too much work to accept flipping of various clauses and cases like "Matěj a Žofie" vs "Žofie a Matěj". Yes, meaning is the same, but there is not much reason to do the flip and the number of the forms that needs to be supported is often huge already. Especially on the Czech side.