According to Lisa Elliott, her sons Bailey, 10, and Harley, eight, had to be treated in A&E due to a red rash, which she believed was due to excessively high levels of hydrochloric acid in the water. The leisure centre has disputed this.
She said Freedom Leisure, which runs the pool, should apologise. She said: "I don't want an apology for myself; I want it for my children. It was my children that have been injured.
"They both have really scaly skin now from where I am still treating them for chemical burns."
The highly anticipated new leisure centre in Sea Road, Littlehampton, opened last Friday. The next day, Bailey and Harley went swimming with a friend and their father.
But according to Lisa, after about 45 minutes they got out of the water because their skin felt itchy, which got worse despite using the pool showers for half an hour in an attempt to soothe the irritation.
When they got home, the 31-year-old from Yapton said Bailey had a red rash which spread across his chest, arms and eyes, and his younger brother was suffering too.
She went to the centre for an explanation, where she claimed a manager told her the boys had burns from their foam floats, which she disputed as their eyes were also red too. She said: "My kids have never had float burns, and they have been to lots of different swimming pools."
As their condition got worse, she took them to A&E, where she said a paediatric doctor eventually took the decision to treat them using antihistamines. "She said 'I am not happy with seeing this as a rash. I'm treating this as a chemical burn'", Lisa said.
"I was seeing red; I was raging."
On Sunday, she saw a post on Facebook that the pool had been temporarily closed, and went back down to ask a manager why this had happened and to seek an explanation for her son's condition.
There, Lisa claimed they told her the closure was due to too much hydrochloric acid in the water, which is used to lower the pH levels in swimming pools, but said it was not linked to what happened to Bailey and Harley.
"I really struggle to believe that," she said.
While Bailey and Harley were on the mend, Lisa said her eldest son, who has autism, is now scared to go in a swimming pool.
She said: "I feel really sorry for him, because he loves swimming.
"I won't go there again, and it will be a very slow process to get my eldest back into a swimming pool."
A spokesman for Freedom Leisure said: "We were extremely sorry to hear that Ms Elliott’s two sons both experienced a rash on the skin after she first spoke with our duty manager last week.
"As per our further communications we have explained that the new pool has an automated system which continuously takes water readings that we also back up with manual checks every three hours, and we have confirmed that at no point during pool opening hours were the levels outside of legislative operating parameters.
"pH levels did rise slightly during the night which is why we delayed opening on Sunday – it is worth noting that it is not unusual for levels to fluctuate especially after a busy session, and that the automated system will rectify this.
"Over the weekend in question we had over 600 people swimming and can confirm that thankfully there have been no other incidents or concerns raised.
"Therefore we believe, and have explained to Ms Elliott, that the location and nature of the rash suggest that friction from sliding on and off pool floats may have been the cause."