Bali for families
Here is a link to the Bali for Families web site that might have some helpful information for you.
My husband and I stayed at the Putri Ayu Hotel some years ago and just loved it. It is at the end of Jl Bisma, a lovely street which runs parallel to Jl. Monkey Forrest. You can walk through the Putri Ayu Hotel to get to Jl. Monkey Forrest or walk along Jl. Bisma to Ubud's main road.
Also along Jl. Bisma is the Uma Sari Hotel which I had a look at during my last trip to Bali earlier this year. This is a small place but the owners were lovely and the outlook beautiful. The rooms were not as big as those at the Putri Ayu but I'm sure you could all squeeze in.
Uma Sari Cottage Ubud - Ubud Hotel Bali.
Hope the links work and you have some good luck with this.
There are a number of other places along Jl. Bisma such as Nick's Hidden Cottages and Nick's Pension and several others that I can't name. Some of these are located off the road beyond the rice paddies and the pathways can be narrow. This may not be the best with children and particularly at night.
I don't want to alarm you but always remember that Asia has some very interesting snakes and Ubud is semi rural so something to watch out for.
Catherine