Looking for single Home to Rent

Few people do month to month, most want a contract, typically 6 months to a year. Have you checked clasificados? I put the URL on the site several times.
Funny how you were looking at Dorado, Bayamón, Ocean Park and jumped all the way to Humacao.
You can also go with a realtor.
You would be best to come look and rent what you want, lots of places do not have pictures or only have a few picture so you don't have the whole story.
Another option is rent an AirBNB which is cheaper than hotel for a week or two, go look for a place to rent, get electric and water connected then come back to the states to pickup the family.

WARNING: Most houses and apartments rentals are basically the wall, floor, and a ceiling. No furniture, a lot of times it may not have a stove or refrigerator. So you need to get those or sleep on the floor for a few days and drink warm water.

Having family on the island a blessing.  Temp housing not need it.

If someone on the Island that knows of any places please let me know.

I'm agree with Rey suggestion, pictures will not be enough to make a decision on a house. Best spend some time looking at places and getting an idea of the areas.
As per rentals, most houses do not include any appliances. And most renters will want at least a year contract. Water and electricity will required a contact to hookup and most likely you will have to do this in person.

I get the ends and out renting and what is required and what will need to be done. I was simply looking for someone that possibly has a lead on properties or has one to rent.

If you are not yet here, I would suggest finding a simple place, rent for six months, while you look for a more permanent home. Most use clasificadosonline.com

I agree try some simple and easy to get place for rent for sometime... then move to the permanent one... It will give you time to research over better options.. and accurate place for your needs..

There are two units available in my condo community but they are in Vega Baja. Well maintained and they have a pool...around $750 - 3 bedroom 2 full baths.

That's really very decent offer.