Not only can you do as many posters have suggested and the OP inquired about, it is the rule for most countries that you must enter/leave that country using the passport issued by that country. So for example, the OP's daughter must use the US passport to enter/leave the US, and perhaps Indonesia has a similar rule requing that as an Indonesian citizen, she enter/leave Indonesia on that country's passport.

Since of course you'll always have both...and both countries allow dual citizenship, shouldn't be a problem.