How can I pick the brain of parents of children aged 2-6 and get them to answer my questions around their pain points in shopping for their kids?

Depending on how much time you have there are two main ways:
1. Have 30 min call with parents and ask them specific questions plus any follow-up questions. [ You will get fewer responses but might get other extra useful information ]
2. Create a detailed survey with questions you would like to get answered. [ You will get more responses to the questions you ask ]

You should try to get a list of parents from your network ( on social media, previous school groups, previous work mates.

There are other options which will require a budget. Happy to answer more questions on a call after understanding your business better.

According to Google, 3.5 billion searches are conducted each day on its platform – 40,000 search inquiries every minute. I would venture to say, that whether you’re searching for an answer to finish up some homework, you’re looking for side hustle secrets to make extra money, or you want to know how to treat a hangnail, many searches, even those that start out with a pleasant goal in mind, such as taking a trip to Disney World with the family, are related to a pain point. For marketers and communicators, pain points are the gateway to introducing a customer to your company’s unique brand promise and experience. Look for WTF experiences among customers and potential customers.
By observing and asking, you can take the guesswork out of understanding a customer’s pain and instead, develop an early-warning system. Such a system is designed to document pain points to provide decision makers the information needed to make better decisions about product innovation, branding messages, and marketing spend. With the internet and social media, for the most part, it is all there, just waiting to be mined by the curious marketer or communicator. Listening to real customers helps build empathy throughout your marketing communications organization and offers a checklist of action steps that you can take to improve your product or service.
Keep in mind, for every customer who contacts your company, there may be a dozen who don’t bother but, instead, vent their pain in public through an online forum, or worse yet, simply give up on your brand and contact your competition. Consider surveying them first – to obtain written input about customer pain points – and then host small group discussions at an event, such as a national sales meeting with a third-party moderator. For example, if you enjoy walleye fishing, there’s an online forum called Walleye Central where anglers share information about fishing techniques, lures, boats, locations, trips, etc. It is not uncommon to find members asking each other for their opinions on different products, or to seek out information from other members about how to fix a problem with a product or service. Other online sources where groups of people converge around specific topics or passions include Quora and Reddit.
Type in a phrase such as “problem with bed mattress” in the Google Search bar. These phrases are based on searches that other people have made on Google, offering clues about other potential pain points.” Design a survey that digs into the pain points that current, potential, or former customers are trying to solve by buying your product or competitive products or services. Some customers will hold back in talking directly with a representative of the company but often are less reluctant to speak with someone outside of the company.
Another source of online surveys is LinkedIn. These survey results often address concerns or issues that your organization can use to better understand customer pain points. In their reviews, customers often share how a particular product or service either did or did not solve a pain point. Reviews offer an opportunity to scout a competitive product.
Go to retailers that sell your product or service and find out how you are treated, just like any other customer. Mystery shopping allows you to test perceived pain points to see how sales associates engage a customer and attempt to solve the pain point. This will help prioritize future messaging and media spending. In exchange, you enter these customers into a drawing for a prize. For example, for a hand cream company, we conducted an online contest in search for America’s hardest working hands and feet.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath