What is the Remillard "gene"?
If we let 'A' denote the dominant "immortality" allele in Remillards of Donatien's line (whatever causes them to regenerate assiduously as Rogi explained) and 'a' the recessive mortal alleles, suppose it's the case that:
Donatien Remillard, Rogatien Remillard: Aa
Elaine Donovan: aa
Marie-Madeleine Fabre: aa (this is not certain, but I'm going to set it forth as a conjecture since Atoning Unifex seems to imply to Rogi that the main reason he's setting her up with Donny, aside from Rogi's sterility, is that she has the right proto-operant alleles to match up with the Remillards - not for any immortality genes)
My hypothesis, then, goes as follows:
Lucille Cartier: aa
Annarita Latimer: aa
Denis Remillard: Aa
Victor Remillard: Aa
Shannon O'Connor: aa
Laura Tremblay: aa (as she was not Victor's child but Kieran O'Connor's)
Paul Remillard: Aa
Teresa Kaulana Kendall: aa
Jon Remillard: aa due to prochronistic mutation
Madeleine Remillard: Aa despite consanguinity
Marc Remillard: Aa despite consanguinity
Cyndia Muldowney: Aa
Hagen Remillard: Aa or aA or AA
Cloud Remillard: Aa or aA or AA
Mental Man: Aa or aA or AA (not aa like Jack; they were born as normal metas of the Remillard line, with similar consanguinity to their genetic cousins Hagen and Cloud, via Madeleine)
Paul Marc-Ange, son of Cloud and Kuhal Earthshaker: Tana knows (hybrids seemed to inherit Tanu longevity, but the Guderian time gate had only been in operation for 90 years or so at the time that Group Green passed through, and Skin was used the same way the regen tank was)
Now, given the number of progeny sired by Donny (10 by Marie-Madeleine Fabre, IIRC), Denis (7 by Lucille Cartier), and Paul (8 by Teresa Kendall, 4 surviving to adulthood; at least 38 total), it would seem improbable that they all turned out Aa or aA. However, we really don't know the homozygosity ratio for the mortal allele - it could be miniscule, meaning that Annarita was just a fluke. She could also be a back mutation, though I think May would have mentioned that if that had been her intent.
The conjecture I've made here, which could be entirely off the mark, is that the Remillard immortality "gene" is an allele that expresses identically in homozygous and all heterozygous descendants of the founder of the line, Donatien Remillard. In fact, we know from a conversation between Marc and Rogi (in Jack the Bodiless, IIRC) that there is variable penetrance, i.e., expression levels. Rogi remarks to Marc that "you're up to your young stuck-up pif in the good stuff".
By the way: for at least the first generation, the Remillard immortality gene must have been quite a damning indicator of paternity! Severin had several divorces, as I recall, and I could see Paul pinning some of his illegitimate children on him, but IIRC Philip, Maurice, and Adrien had stable marriages. As May pointed out, though, Teresa knew all about his philandering, so it was rather a moot point save for angry husbands such as Rory Muldowney.