Yes, there are other issues than simply having some wine.
There is a difference between drinking for enjoyment and drinking to cope. Someone disclosing they feel they need alcohol to get through the day, suggests an unhealthy relationship with alcohol and that they're struggling with something.
The situation includes covert drinking - the alcohol has been concealed. Concealing how much alcohol is being drunk can be another sign of an unhealthy relationship with alcohol.
People who have healthy relationships with alcohol would not drink to the extent that they "reek of booze" (as per the OP) while having primary/sole responsibility for their children in a public place in daytime. To "reek" of it, someone needs to have quite a bit. Think about how much alcohol means someone exceeds the drink-drive limit - that limit is there because alcohol is known to impair judgement, risk awareness and reaction times. Now consider that it takes quite a bit more than that to "reek" of alcohol.
So, we have indicators of reliance, secrecy and prioritisation of alcohol. Which are all markers that the woman in question may be struggling with an alcohol problem. If she has an alcohol problem, that places her at risk and her children, as well as the wider 'ripple effect' of consequences for others.
If you notice signs like this in your own behaviour or the behaviour of others, you shouldn't ignore them or assume it'll be fine. Getting help at an early stage can make a big difference for outcomes.