My clients were ready to proceed. The other realtor sent a cashiers check to my brokerage.
Why did he/she do that (given that no lease was signed)? What does "ready to proceed" mean?
They waited several days and could not receive a response
Who are "they"? What does "could not receive a response" mean? Receive a response from whom? About what?
Finally 3 days later the lease gets signed by the prospective tenant.
Is this 3 day period part of or in addition to the "several days" mentioned in the prior sentence?
The homeowners . . . are refusing to sign anything with this prospective tenant.
Why?
The other realtor is claiming the 3000 cashiers check sent to my brokerage was a deposit and means the lease is accepted?
Despite your use of a question mark this sentence is not a question. If you intended a question, I'm not sure what you intended to ask. If you're asking whether the other realtor's assertion is correct, it is impossible to answer that based only on the facts you have provided.
They claim they are going to sue me in court and this is illegal.
I'm not sure what "this" refers to or who "they" are (when you use "they" to refer to everyone in a story involving lots of people, it gets confusing fast).
I . . . wanted to check for advice
Legal advice does not come from anonymous strangers on the internet. We can give you some feedback (if you provide clear and complete facts), but we cannot properly provide legal advice. If you have legal concerns, you should consult with a local attorney.
After several days with no signed lease and very little communication about what was going on, the homeowners elected to go with a different applicant.
Was this clearly and immediately communicated to the first prospective tenants and their realtor?
Thanks for all the advice. You guys are awesome.
Are you the original poster posting under a second screen name?