This will make your head spin more.
Parents of Hans Madsen Kok were Else Lorentsdatter and Mads Hansen [per Flemming's finding in the churchbook].
From that I found a website that discusses this family and includes photographs of their home.
Most of the information is in Danish - I'm not the best person to translate for you.
Here's a long description (in Danish) of the farm where Else Lorentzdatter and Mads Hansen (Kok) lived, LINK:http://www.ocpd.dk/mixpix/koch/Jorgens%20side/Gaarde/saeding...
You can see that the Else Lorentzdatter first lived here with her second husband, and then when he died, she lived here with her third husband Mads Hansen Kok.
I hope Google translate will work, or someone who speaks Danish can help. Also try GramTrans (gramtrans.com)
More below, about the mother of Hans Madsen Kok. LINK at bottom:
Parents: Lorentz Henningsen (258) og Ellen Olufsen (259) fra Tirsted
Baptized: 7/4 -1747 in Tirsted kirke
Confirmed: Tirsted kirke - 1763 d. 10/4. (1761 en pige ved samme navn konfirmeres i Bursø kirke men det er næppe hende)
MARRIED 3 times:
1. 1766 d. 15/12 Christen Pedersen - født i Tirsted. Døde 1767.
2. 1770 d. 8/6 Jørgen Christoffersen Kok i Sæddinge. Døde 28/12 - 1782.
3. 1783 d. 6/2 Mads Hansen (Kaare)(Kok) in Sæddinge. Born 25/3 - 1756 in Taagerup, died 21/2-1829 in Sædinge.)<-----
9 CHILDREN. Three of these were with Mads Hansen (Kok), including:
Hans Madsen (Kok) born 20 March 1785, died 05 May 1851
De boede (where she lived):
Store Sæddinge på en gård. (på en gård = on a farm, I think)
Stilling (occupation): Madmoder
Died: 28 March 1816. She was about 69 years old.
This biography of Else Lorenzdatter continues here (in Danish):http://www.ocpd.dk/mixpix/koch/Jorgens%20side/129_Else_Loren...
All the above as found by the creator of the website and not researched by me.
Pedigree Style Family Tree shows parents and grandparents of Else Lorentzdatter, going back to the 1600s. Click on each name to see a biography of that person. LINK:http://www.ocpd.dk/mixpix/koch/stamtrae.htm
Modern map [kort] of the area around Sædinge: http://www.ocpd.dk/mixpix/koch/syd_lolland.htm
Included on the above website is an introduction to "Slægten Koch/ Kok" [Koch/ Kok Family tree]http://www.ocpd.dk/mixpix/index.htm
Where the name Koch/Kok came from:http://www.ocpd.dk/mixpix/koch/navnet_koch.htm
and a few descendants today:http://www.ocpd.dk/mixpix/koch/familien_koch.htm