It really depends on the exact circumstances and laws (sometimes just leaving the city limits changes the rules, which means some small cities have "sex offender districts" right over their borders.) But I don't think there's any case where someone with kids moving in next door would force someone who already had housing to move (Although there are definitely cases where a sex offender moving *in* causes custody issues, and if LW and spouse are thinking of adopting or fostering it's definitely worth checking into what the agencies they're applying with a might think of that before they make any decisions.)

What often causes the issue is rules about being near schools - it's pretty common for sex offenders to be banned from, say, living within two miles of a school, in an area where schools are on average three miles apart from each other, so there might be a total of one acre in the entire county where it's technically legal, and it's a weird corner of forest with no access roads.