you can replace the word "thought" with guess. In American English, "I thought" most of the time means nothing. it is often a way to begin a sentence.
In this case, actually the mother wants the husband to help with the dishes. (In USA hsubands washing dishes are very common even though we got machines; but small loads are done by hand -- not to save money, but to be GREEN with the environments = save water.)
the key here is "she gave me the idea" That is mom's idea that Dennis is to help.
Dennis the Menace is known for breaking things. The Mom wants the dad to see and get the picture that HE should help out.