2 separate ceremonies

If you do your civil ceremony first you can later do what is called a convalidation in the Catholic church which is a ceremony done when a marriage ceremony was not performed in the church for whatever reason and is a blessing that will make your marriage valid in the eyes of the church

You may want to consult with your priest about this. The Catholic church can be very strict in it's guidelines/rules, and you don't want to lose the opportunity to get married there. First, if you want to be married by a Catholic priest in your church, you'll probably have to do that first, since, if you get married somewhere else first, it won't be by the Catholic priest/church, and it would be considered a "vow renewal" more than a "marriage ceremony."

I think it's fine to do both, if that's what your families want. But I would make sure you know the requirements of your church before doing anything.

Is it important for you and your fiancé to get married in the Catholic Church? If it’s only your parents wishes I would tell them too bad.

So there's a lot of things here
First and foremost if you and your fiance don't want to get married I the church you shouldn't feel pressured too.
Also some churches have attendance and marriage counseling guidelines that need to be met in order to get married by the church, you should check and see if you meet them.
If you think they're strict I'll guess and say they won't let a second preform the ceremony at the outdoor location then (unfortunate).
Overall you should probably do the Catholic ceremony first because preists can sometimes get upset or confused when couple's don't do the actual wedding with them, unless it's convalidation of marriage.
If you do the Catholic wedding first be sure to tell whomever is conducting the other ceremony so they don't file two marriage certificates.

Ugh auto correct!
Won't let a deacon* preform outdoor ceremony