Here are the parents in the 1865 census (Maline is about 16 and not listed with parents):http://gda.arkivverket.no/cgi-win/webcens.exe?slag=visbase&a...
Bakketeigen gard, Thingvold Prestegjeld, Øre sokn, Møre og Romsdal
Ole Ols., husfader, occupation husmand med jord, married, age 48, born about 1817 in Thingvold
Beret Pedersd., his wife, age 40, born about 1825 in Thingvold
Ole Ols., their son, age 20, born about 1845 in Thingvold
Iver Ols., their son, age 5, their son, born about 1860 in Thingvold
Beret Olsd., their daughter, age 3, born about 1862 in Thingvold
1910 census (posted earlier), living with Malina Olsdatter and husband Ole Samuelsen, Myklebostad, this is probably Malina's mother: Biret Pedersd. Bjerkeset, widow, forsørges i huset, born 31 July 1821
1900 the (likely) mother is Biret Pedersdatter, H. til Famelien, widow, Husgjerning, born 1820 in Øre, Rom (abbreviation for Romsdal, presumably)
Alternate spellings of Bjerkeset: Bjerkeseth (1875 census) and Bjerkesæth (1865) and
Birkesett, Birkesætt, Bjærkesætt found here:http://forum.arkivverket.no/topic/90596-4638-tingvoldgjemnes...
Some history of how Gjemnes is related to Tingvoll/Thingvold:http://en.wikipedia.org/wiki/Gjemnes
In 1865 census, Malene's sister Beret Olsdatter is age 3, born in Thingvold.
The record of Beret's confirmation (20 Sept 1878) says Berit Olava Olsdatter was born 28 February 1863 at Birkesæt in Thingvold. Parents Ole Olsen Birkesæt and Berit Pedersdatter.
(Look at the record on the link to see what spelling of Birkesæt is used; I find it hard to read.)
Source: Øre i Tingvoll, Møre og Romsdal fylke, Ministerialbok nr. 584A06 (1869-1878), Konfirmerte 1878, side 134. See #49:http://www.arkivverket.no/URN:NBN:no-a1450-kb20070109310501....
And here is Berit's birth record: Berit Olava born 28 February 1863. Parents farmer Ole Olsen Birkeset and Berit Pedersdatter. To the right you'll see a list of baptismal sponsors that includes a John Pedersen, Gaupset (a possible brother to Berit Pedersdatter). The record says the baby Berit was baptized at home.
Source: Øre i Tingvoll, Møre og Romsdal fylke, Ministerialbok nr. 584A05 (1857-1868), Fødte og døpte 1863, side 51. See entry #31.http://www.arkivverket.no/URN:NBN:no-a1450-kb20050615010055....
Presuming Malene lived with her parents at Birkesæt in 1863 (when little Berit was born) or earlier, this would explain why this farm name is attached to Malene in your aunt's records.
Here is the record of another baby Berit Olava Olsdatter born 07 June 1858 to (presumably) the same couple. It was customary to name a child after an earlier child who had died. The record is especially useful for noting the baptismal sponsors; they might be relatives of the baby's parents. http://www.arkivverket.no/URN:NBN:no-a1450-kb20050615010017....
At the baptism of Maline's sister Berit Olava Olsdatter in 1863, we found a baptismal sponsor named John Pedersen, Gaupset (sp?) and speculated he could be the brother of their mother Berit Pedersdatter. Seeking John in the 1865 census, we find a John Pedersen at Gaupsæt with a Maline Olsdatter (of the right age and birth place) living there also. And also John's parents are in the household - so they could be the maternal grandparents of your Maline (needs more research to determine).
Gaupsæt farm, Thingvold Prestegjeld, Øre sokn, Møre og Romsdal fylke, Norway
John Pedersen,, husf (husfader = house father) occ. Gaardb. Selveier, age 41, born in Thingvold
Daardi Evensdatter, his wife, age 41, born in Thingvold
Peder Thorstens., hired worker
Anne Thorstensd., hired worker
Malline Olsdatter, hired worker, age 17 (about 1848) born in Thingvold <-----------------------------------
Peder Pedersen, his father, occupation Kaarmand, age 75, born in Thingvold
Sigri Iversdatter, his wife [Peder's wife], age 72, born in Thingvold
Johannes Olsen, foster son, age 11, born in Thingvold
Serianna Olsdatter, hired worker, age 19, born in Thingvold
Now the other people named Olsen/Olsdatter could be tracked back, to see who are their parents. They might be siblings to Maline (needs more research).