Why do Pam and Ned have such a hard time finding housing?

There are a number of reasons. For one thing, they're both drug addicts. Pam has made efforts in the past to stay off drugs, but without success. The couple's drug addictions have landed them in hot water with the law. They've both served time in prison for drug-related crimes, and this also counts against them as they search for a new place. As well as a lengthy rap sheet between them, Pam and Ned have also racked up an extensive list of evictions. Such a bad record indicates to future landlords that they're untrustworthy and can't be relied upon to pay the rent. In fact, they're evicted from Tobin's trailer park because they owe him around $3,000 in unpaid rent.
The biggest challenge that Pam and Ned face in finding a place to stay, however, is that they have children. So many landlords just don't want to know as soon as they discover that the couple has kids. Children tend to cause wear and tear on a property, so landlords are often reluctant to rent out to families with kids. Pam has two children with Ned, two from a previous relationship, and another baby on the way. This makes it all the more difficult for them to find somewhere to live.