Being her husband is your strongest argument, and it is worth pursuing through the right channels.
Standard visitor approval runs every applicant through a criminal background check, and a felony conviction combined with active probation will block approval through the normal process. That is the automatic result and it is not personal. The system flags anyone with a record, and someone on probation for the same crime that put their spouse inside is going to get denied at the standard level.
The path that actually exists for your situation runs through the warden's office. A special visitation waiver can be requested, and the spousal relationship is the most compelling case you can make for one. Facilities do grant these, particularly when the request is handled respectfully and the circumstances are straightforward.
Call the warden's office directly. Be humble, be honest, and keep the ask simple. Explain that you are her husband, that you are on probation and understand the standard process will not work, and ask what steps you need to take to request a special visitation approval. Let them guide the process from there.
One important step before any of this is a conversation with your probation officer. Visiting a prison while on probation requires their knowledge and in most cases, their explicit approval. Going without telling them is a risky violation that could send you back inside, which helps neither of you. Get it on the record with your PO first, then pursue the warden's waiver with that clearance behind you.