Well this is currently impossible to do as the other half refuses to believe this.
No it’s not. My wife is Jewish and refused to have a convalidation. So I simply received a Radical Sanation instead.
What the Radical Sanation does it confirms that you understood what marriage is at the time of your wedding. Then, you are basically granted a retroactive dispensation.
You would not be remarried. The Church would retroactively recognize your marriage just as if your had received a dispensation.
NOTE: it sometimes takes a little bit of waiting because the Church prefers your to receive a convalidation. So a priest might ask you to pray on it for a while and determine if there is not way to convince your spouse to convalidate (but the priest will NOT want you to hurt your marriage).
The Radical Sanation can be just you, if you spouse wants nothing to do with it.
If your spouse does not participate, the Church will simply ask you to inform you spouse that you promised to do everything within your power WITHOUT HURTING YOUR MARRIAGE to teach your kids the Catholic Faith. But if the spouse say no, the spouse comes first. You just have to do whatever you can HONESTLY do without hurting your marriage.
If you have questions, feel free to ask me. Like I said, my wife is Jewish and a little anti-Catholic.