As others have stated, we are sorry for what happened to your daughter - it was an unfortunate accident.
But from what you have written, it sounds like you are blaming the lifeguards for not watching your child. As you stated, your daughter was going up the wrong way - (1.) she is old enough to know better and, (2.) you do have to realize that the lifeguards cannot be sitting by watching an individual person the whole time. Lifeguards are there for everyone. They are not there on a one on one basis. And from what you stated, there were more than one person there at the pool which the lifeguards also have to take into consideration.
And, like all accidents, it probably happened quickly.
If you were there or your husband, then you are responsible for your own child. You do not bring them to a pool and expect the lifeguards to be babysitters because that is not what they are there for. If you were not there supervising them, then maybe you should have been so you could have taken the corrective action when it was being done - basically, telling your daughter than is not appropriate to climb up a slide and if she does it again, she will not be allowed to use it.
At a playground, if your child is playing on a slide wrongly, it is your duty/responsibility to tell them not to go up the wrong way - to use the stairs. As a parent, it’s your responsibility to tell them that there are consequences from their not using it properly - i.e. falling/getting hurt. If they continue doing it, then that is something you should be addressing with your child.
There are far too many people out there suing others because of their own neglect and failure to be responsible for their own actions and that includes the action of our children. Accidents happen. It’s a hard lesson for your daughter to have to learn but one that obviously she will remember and so will her siblings.
Hopefully, everyone learns from their own mistakes. I'm sure you have in the past, and so have I which is why I tell my children that the stove/oven is hot and it hurts; that you don't run with things in your mouth, you can fall and get hurt; that scissors are not toys, they can cut and you will hurt and bleed; etc. etc.