If you want to visit the Theme Parks with your children whilst in Beni, (as I'm sure you will want to) then I would agree with Sanji and go in May, as these places do tend to either close completely, like Aqualandia,(thats the water park up near Mundomar), or reduce their hours towards the end of the year. The Summer and Winter seasons in Beni seem to take place litterally overnight.
Terra Mittica will probably only be open at Weekends in October (at least it was only open weekends when I was there last October). Mundomar, I think thats open all year round except Christmas Day......but again it would be best to visit in May, as the park is set on the side of a mountain, and it can get very chilly up there sitting on the concrete watching the shows.(they used to supply little rubber mats to sit on, but they don't anymore for some reason).
I'm not too sure about the opening hours for Terra Natura, but to be honest if you can't get there you will not have missed anything really. Its just a gloried zoo, (and not a very good one at that) and as an animal lover I found it very depressing

and upsetting

.....anyway, I digress. I'd take Sanji's advise if I was you and go in May, simply because it will be a lot warmer and all the Parks will be open.
The Oudoor Market is open all year round. Some of the pubs and clubs close up towards the end of October, but there is an abundance to choose from so that should not pose too much of a problem. The swimming pool at the Helios Hotel is covered and heated in the Winter months, and is open to non residents at a very small nominal charge.....3€ I think.
In addition to this, if this helps you to decide, Benidorm's clientelle tends to change towards the end of the year, and is populated by the more senior hoiliday makers.....there are still children around but not so many I find, as there are in the months at the beginning of the year.
All in All, baring your children in mind, I would definately opt for May, rather than October......but as they say.....
the decision is yours
Have a super holiday whatever you decide