First the marriage date (Eunice House to Thomas Loveland) in 1705 doesn't seem to be in the vital records which doesn't make it wrong, but suspect. In addition they seem to have had children whose estimated births were before their marriage.
This https://books.google.com/books?id=niQ3AAAAMAAJ&pg=PA17#v=onepage&q&f=false says she was the sister of William who married Hannah House. and cites Glastonbury Cen. p. 191
Here p. 191 (image 193) need to sign in at Family Search - free) https://www.familysearch.org/library/books/viewer/401314/?offset=0#page=193&viewer=picture&o=&n=0&q= so called Glastonbury Centenial claims Eunice House m. Thomas Loveland was a daughter of William House who also had children:
- John m. Eunice Fox 1703;
- William m. Hannah Loveland 1709;
- Joseph m. (1) Hannah Porter & (2) Rachel Pitkin;
- Eunice m. Thomas Loveland;
- and perhaps Sarah m. Joseph Smith 1696.
This, off course does make her a sister of Joseph House-1125. However, it's wrong. She was not the sister of Joseph House-1125, or the William who married Hannah House. Joseph and William's siblings are well established. The reliable genealogist Donald Lines Jacobus in Hale House and Related Families pp 328, 329 has given an abstract of William Sr's probate and listed the living children named on his Inventory (taken 22 Feb 1703/4) with their ages:
- John House (30),
- Sarah Smith (28),
- Mary Hale (26),
- Anne House (2?),
- William House (19),
- Joseph House (16).
The names John, William, Joseph and Sarah repeat on both lists, so we're talking about the same father William Sr., but there was no Eunice mentioned in the inventory, which would legally would have included her. Even if she had been deceased, her heirs would have been mentioned.
Additional source for William Sr's probate, Manwaring's Probate Digest. https://archive.org/details/adigestearlycon01manwgoog/page/82/mode/2up
Of course, none of this solves the problem of who Eunice's parents were, but we know they were not William and Sarah (Bidwell) House. Because of the proximity of Wethersfield and Glastonbury, it does seem logical that she was somehow related to this family, but at this point there doesn't seem to be evidence of that relationship.