Breach of Contract - any ideas how to resolve?

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Our tenants’ lease just renewed in May for one more year. Just after it renewed, we found out that there are two unauthorized occupants, both with misdemeanors and additional pets. We asked one of the tenants to resolve the pet issue verbally, but the pets are still there. We just found out about the extra occupants and that they have been there for 3 months. My partner wants to write them a letter to resolve both issues and proceed with eviction if unresolved. I was thinking of asking them to give us an increased month’s rent deposit along with their own 30 day notice if not resolved (at this point I’d be willing to let them out of their 1 year lease early). Is there a different angle we could take?