Long term rentals in Ubud Bali

I've been living in Ubud for the past 21 years. 

In town long term leases are considerably more expensive for the simple reason that these properties yield far more income by renting short term to tourists, who very often also want to be right in town.   

My best advice to you is to wait until you and your daughter are actually here, in Ubud, and get to know the area, as well as to get to network with other expats and local Balinese.  Very often the best deals to be found here are by word of mouth.  Moreover, nothing beats being able to physically inspect the property and the neighborhood personally.

Good luck on your move to Ubud!

Thank you! That is the plan. We may rent a place a 10 minute scooter ride away from the city center to be away from noise and traffic. Do you know if there is any place to rent a quad monthly instead of a motorbike? I would feel safer transporting my daughter on a quad, especially during monsoon season. Is it legal to drive a quad on the roads?..

I've seen all sorts of motorized vehicles on the roads of Bali, but I can't recall any quads.  Maybe consider a small Jeep (Jimny).

As far a road noise goes when living "in town"...most all places are down small gangs off of the main roads and you'd be surprised how quiet they are.

I've never seen a road legal quad out here but there are several trikes.
There's no reason you couldn't fit seats in the cargo space and use one of those.
One note, the ones I've seen are all drum brakes so slow is good.

I was afraid they may not be road legal even though I do not know why they wouldn't be? Are they not fast enough?

What are drum brakes? Three wheels might be fine...