@Wes Brand @Matthew Kreitzer @Emmanuella Broadhurst - First Wes - I don't think anything I said is totally against the law - I did not give any legal advice and not everywhere is there limits on rent increases - In most areas, I know of there are none. To Matthew, no one has to be a licensed attorney to give suggestions of law. Or to discuss a sort of legal question, as we are here.
As Emmanuella feels no one here answered her legal question "Can she do this?" And the answers to it were, go seek further legal counsel and that was the best answer anyone could give her. And my responses none of them were of a legal magnitude - towards her question.
My suggestions to landlords and they are suggestions and others have joined in here now - that you have an additional persons or an additional pets clause in your lease. If you are on a month to month basis with a tenant and no lease, then they should be required to sign @ least a renters agreement of some sort, spelling out their responsibilities and limitations and any and all other addendums that may apply such as additional persons or pets.
One of mine is "no waterbeds" especially in older houses. There is no guarantee that the floor will hold the weight of the bed and if that thing for some reason bursts could cause a fire.
Now back to Emmanuella - there are many things you are not saying, once again. Like the size of the home or apartment. What sort of damage there is as far as pets are concerned - a lot of dander around, etc. "facts - landlord talked to you, landlord wants an addtional pet deposit, she is raising parnets rent and wants an additonal $300 from you - you were there 3 years with husband, kids and dog" and from what I can see in your area there are no caps on rent increases - "Florida and her cities have no rent control ordinances", Stephen K. Hachey, P.A. - so assuming this certified attorney in FL is correct, "Yes, your landlord can do this!"
We all have our problems - I have two kids that are ADHD, certified and see psychiatrists often - the one was so severe that it almost incapacitated me totally. Doesn't have anything to do, with where or how I choose to live. What does have a baring on where I live is the amount of people and animals in one house. And whether or not that house is accommodating to my situation. Next, you do not say who pays the utilities there, the landlord or your parents or you for all that matter.
You have a lot of options - move with your parents, husband, kids and animals in tow. Or stay put and try to work things out with the current landlord. Again, coming at you in the manner she has, there is no doubt some sort of problem. But, you are not saying what it is. And your question was answered right off the bat - no lease, yes the landlord can do it - I think you got that answer twice as soon as you posted here.
Next, no rent control's in FL or it's cities. And as far as you moving and paying 3 rents, I only see two - "parents" and "yours" and one might suggest, that you find a larger place and take your whole family with you. But, before you go - make sure the new landlord is Okay with your entire situation, (kids, dogs, parents, husband, etc.) Cause I am not the only one that feels there is some sort of problem that your current landlord is not happy with.
Disclaimer: Nothing here is intended to be legal advice. It is offered solely as a discussion and some suggestions. Any assumptions made are not personal but are on a general scale or what it seems like and personal opinions are not personal attacks. Again, in reading. Florida Law does not prohibit large increases in rent and has no rent controls.
Now, on a more personal note - from what you are saying you need to go before the first or pay higher rents - since you have taken the steps to join here, I suggest you read and read some more, before you go looking for another place. It may help you turn your situation around. That is, instead of finding a Single Family Home, find a duplex or something to house your parents in one side and your family in the other - instead of renting purchase it. It will be yours, no more landlords! Etc., Etc.
If however, you end up staying past the first, so be it. You pay a little more for a moment, til you find the Real Estate Situation you want. If as @Justin Fox has suggested, you responsibly saved your money, you will have no problem doing any of this. I am really, really sorry to hear of your dilemma and do not mean to seem callous, I am not. Sometimes you need to hear things you just don't wanna hear but need too. Again, nothing here is offered as legal advice - you either take the idea as suggested and run with it or not!