It's a problem from a Jewish law perspective if the service is taking part in a church.
There's actually an article which discusses the topic on Chabad which can give you some insight.
In terms of specific citations for this rule:, they cite Shulchan Aruch, Yoreh Deiah 150:1; Shach, Yoreh Deiah 149:1; Darkei Teshuvah 150:2; Igrot Moshe, Yoreh Deiah 3:129:6.
You're not actually supposed to enter a church at all if you're observant. Churches are houses of foreign worship and they specifically teach idolatry in violation of Jewish law (in relation to Christ, the trinity, and so on)
Attending the wake or burial of a non-Jew isn't a problem onto itself. It's a sign of respect and loving kindness for the deceased and their family. The issue comes with the location and what you might be asked to participate in.
Some funerals and wakes are simply social events. The person may or may not have been religious but the burial itself is simply a place for friends and family to come together and remember the individual. There's no religious conflict in this situation for the most part. (if it's not in a Church)
Some funerals and wakes are full blown services. A catholic funeral is a service within which all members of the attending take part in certain prayers and certain ritual observances which a Jew cannot take part in. Even being in that situation passively is still you taking part.
When it comes to honoring and obeying your parents (which is a standard of law), you aren't required by Hashem to honor a request to do something that goes against Hashem.
In this situation, if you were being requested by a parent to attend the funeral service of a family member to appease the family, you are not required to do so as honoring your parent is voided. You simply have to reject in a respectful manner.
In terms of specific citations for this rule: Yoreh De'ah 240:15, based on Leviticus 19:3 with Rashi. This includes posthumous requests, such as to cremate the parent's body (Achiezer 3:72, based on Maimonides – Avel 12:1), or not to say Kaddish (Yabia Omer, vol. 6 – YD 31:4).
If this is a personal conflict within yourself and you feel that this person was someone you loved or respected and wanted to be there to support family and friends, I'm sorry to say that you wouldn't be excused.
In terms of what you could do realistically?
If you have the ability to attend the social event situations and not actually enter the Church or take part in the religious situation surrounding the ceremony, you wouldn't be in violation.
If the whole family is meeting at someone's house after the service and you met them there after the fact, you'd be attending without the religious conflict.
If you make the choice to violate the rule (which is between yourself and Hashem) then that would be your decision. I can't pretend that a situation like this is easy (even under normal circumstances) but at the end of the day, you need to be able to live with yourself and have peace with yourself.
Praying your family finds strength and peace if you're asking about a personal loss.
Barach Dayan Emet.