Firstly, it’s essential to understand that prolonged exposure to damp conditions in basements, such as where you store toys, can indeed trigger or exacerbate respiratory problems like coughing, sneezing, and other allergic reactions among your kids. In Dubai, we’ve seen similar cases due to the high humidity levels during certain seasons.

When addressing this issue, it’s crucial to inspect for mold growth thoroughly. Look out for signs such as discoloration on walls or ceilings, a musty smell, and visible spores. Mold can grow in unexpected areas like behind baseboards, around pipes, or in corners where there is moisture accumulation.

For your situation, given the persistent dampness despite using a dehumidifier, it’s highly advisable to seek professional mold inspection services. In Dubai, companies like Saniservice (contact 800-MOLDS or email hello@saniservice.com for expert assistance) can provide comprehensive assessments and remediation plans.

To manage the immediate situation while awaiting professional help:
1. Ensure proper ventilation: Open windows if possible to allow fresh air circulation.
2. Increase dehumidification efforts: Use dehumidifiers more frequently, especially during wet seasons.
3. Clean surfaces regularly: Wipe down walls, floors, and toys with a solution of water and detergent to reduce mold spores.

Implementing these steps can help mitigate the risks but won’t replace professional intervention. Remember that certain molds can produce toxins (mycotoxins) which might pose health hazards even in small quantities over time.

In conclusion, addressing dampness promptly is key not only for maintaining a healthy home environment but also to prevent potential legal and health issues associated with mold infestations in the UAE.