Thanks for inviting her to your daughter ‘s birthday party. Unfortunately, She could not join as we are on the trip at that time. klingt das natürlich?

Thanks for inviting her to your daughter ‘s birthday party.
> Thanks for inviting her to your daughter's birthday party.
＊　No space after * 's *

Unfortunately, She could not join as we are on the trip at that time.
> Unfortunately, she cannot come as we are on a trip at that time.
＊　after * , *, capitalization is not needed.
＊　"could" is past tense (we want future tense)
＊　You can "join" a party, but usually we "come" and "go" to parties.

>> (より自然に) Unfortunately we will be out of town at that time so she will not be able to come.

参考になれば幸いです。