OK, you seem want an all-around lens to use in a not-gentle environment. And you want to shoot your daughter playing at the beach.
If your daughter is 1.5m tall, and you hold the camera in landscape mode (horizontal) and use a lens zoomed to 250mm, your daughter's image will be as tall as the frame when you are 24m away. Step back a couple meters more so as not to cut off her head when she jumps around! Or zoom out a little, so she doesn't quite fill the frame. If you use a lens zoomed to 300mm, your frame-filling distance is about 30m. With a lens at 135mm, the distance is about 13m.
[How did I get those numbers? I googled for
IMAGE.HEIGHT FOCAL.LENGTH and found
this focal length calculator. Easy, eh?]
I mentioned the numbers 135, 250 and 300mm, because those are the upper limits of some popular zooms. These include the Tamron or DA18-250, DA55-300, and DA18-135. (3rd-party lensmakers also make zooms in similar ranges, but I'm not familiar enough to mention any.) The lenses whose wide ends are at 18mm can take much wider-angle shots than can lenses whose wide ends are 28 or 55 or 70mm. I dislike 55-300mm zooms alone because they are just too long to be general-purpose tools; so if you want wider shots, you must change lenses, which you said you want to avoid.
If you want to photograph your daughter from not-too-close, like 10-15m away, than a DA18-135WR (weather resistant) AF (autofocus) zoom would be an excellent choice. I think the typical cost is somewhere near US$500. If you want to shoot from further away, or to capture faces from a distance, the an 18-250 is just right. Similar (but slightly shorter) 18-200mm lenses also exist. Some of these are no longer made but are widely available on the used market. Typical prices are a bit less than for a new 18-125WR. Although not labeled as WR, they still seal tightly to the camera body.
Yes, budget is important; it controls which of your dreams and desires you may fulfill. Good modern AF zoom lenses, new, are usually not cheap. Older (used) manual-focus zooms may be inexpensive, but usually do not match modern optical quality. So, think about money and distance; and think about the lensmakers Tokina, Tamron, and Sigma; and keep asking questions!