According to my copy of "Thomas Mudgett of Salisbury, Massachusetts and His Descendants", Page 121 states that Herman W. Mudgett married at Alton Bay, N.H. on 7-4-1878 Clara A. Lovering, daughter of Samuel and Lucy Grace Lovering (Lovering: who later married John S. Peverley of Canterbury, N.H.) had Robert Lovering Mudgett, born in Gilmanton N.H. 2-3-1880.
Page 142 states that Robert Lovering Mudgett died 11-3-1956, New Smyrna Beach, Florida. He married (1) on 10-19-03 Alexandra Gilbert b. 1880), (2) Mary Griest.
You are aware of the fact that Herman W. Mudgett was a known criminal and very infamous due to his actions, aren't you? An early edition of the Guiness Book of World Records lists him as "the most prolific murder known in recent criminal history." According to a book written about him by David Franke, he (Herman) eloped at the age of 18, marrying Clara A. Lovering before the justice of the peace in Alton, N.H. Clara was his only legitimate wife.
I'm sorry I don't have any more information than the above. Good Luck on your search.