My mum is very Catholic and wants me to have a Catholic priest at my wedding

Why not have religious elements, such as music, a prayer, a reading, etc.

Or have a Religious Celebrant (see the Federal Attorney General's Celebrant List for this category of Celebrants).

The short answer is yes. You can have a priest present who could offer a blessing along the way as the ceremony is performed with the rest of the body of your ceremony can be built around you and your partner.

given you want some Catholic elements you can combine the two, you could have a celebrant and a priest play parts in the ceremony, you and your partner would decide who does what, or you could just have a celebrant and have some Catholic based readings

In short, yes you can have a catholic priest involved alongside a civil celebrant, or even catholic sentiment/ceremony infused in the ceremony.  You may find yourself involved in much compromise here though which in turn may be moving away from what YOU and your partner want this celebration and experience to be.  Rather than being overly concerned with what it is your mum wants.  For mine, front and centre is what the couple want as that is who I would be working with and for.  And then there is finding a religious celebrant that may (or not) be less willing to compromise - but this is not my wheelhouse and you would of course need to look to bring the religious celebrant alongside.  That said, there are many civil celebrant's who are of a religious bent that could well be the compromise that keeps most people happy. But then I go back to my basic tenet - it is about what the couple are looking for.  No doubt Mum will likely be happy with whatever ceremony you decide.

Many Celebrants such as myself are Catholic and would be happy to include prayers or readings.

My mother was a devout Catholic but the first of my ceremonies she attended, she loved.

There are also a small number of independent Catholic priests who are not tied to a diocese and hence are registered as Civil Celebrants but still consider themselves priests. 

In addition, I have conducted a number of ceremonies where the chosen 'Minister' was not a registered Marriage Celebrant and so I stepped in from the wings to solemnise the marriage which allowed the minister considerable freedom in his part.

There are also some churches that can be hired for weddings conducted by Civil or religious Celebrants.

It is of course very important that you and your partner are in agreement as to what will be included and who your Celebrant should be.

Marriage is a partnership and you should both be able to enjoy your ceremony.

Hello Bride

Celebrants are trained to give you as a couple the beautiful ceremony with all the  elements that you want on your special day, including any religious components  It is a ceremony to join you and your loving partner as well as two families, but it is your ceremony, so you and your partner must agree on all of the ceremony and sign this off with your Celebrant.  If your Mum feels including religious elements  in your ceremony is not enough for her, perhaps you and she can do something religious such as go to Mass together the weekend before your marriage.   Wishing you a wonderful cermony and a very happy life with your partner.

You can absolutely include religious elements in a civil marriage ceremony. You may choose to open with the Lord's Prayer, have a Bible passage or other blessing read by a loved one, or take part in a ritual such as a ring ceremony. You and your partner could opt to recite the traditional Catholic wedding vows, alongside the mandatory legal vows - which your celebrant will explain to you!

I feel as it's your special day and should be a reflection of what the two of you want.

As a Celebrant I would encourage the two of you to consider that your married life will be filled with compromises so maybe this is the start of how you both negotiate this particular compromise.

I think if you want some Catholic elements then you can incorporate them and invite your partner to include something that he would like. 

Your planning can then be a win / win for all and you can both enjoy the day equally. xx

Hello

Incorporating both a Catholic Priest and an Authorised Marriage Celebrant is accomplishable, however, depending on if you are going to get married in a Catholic church setting, you will need to ask permission from the Priest of that church if they are happy to have this arrangement. 

Also establish who will be responsible for the legals to the marriage (either the Celebrant or the Priest)?

Sometimes it can be very challenging to please everyone involved

Its always very hard to make everybody else happy when it comes to your wedding. It is a day for you both to enjoy and make your promises to each other. A celebrant can add many things into the cermony such as blessings and prayers. The right celebrant can bring different elements to a ceremony that hopefully will satisfy you both on your day.