Unfortunately, yes if you have given a guarantee and can't get money from your ex-husband. Talk to the bank before giving up your transport. Using hardship, they may give you time to straighten out the problem before they take steps to recover their loan. If on talking terms with your ex-husband, maybe see what he is willing to do.
You may need to consider how the property is going to split overall.
To add to what Rod said, there's generally no such thing as 'primary signatory' on a loan. If you're both borrowers, it will undoubtedly be joint and several liability - meaning that either, or both, of you can be pursued for payment. If you're a guarantor, which is different, you can only be pursued if the borrower has failed to comply with the loan terms.
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