The genetics of handedness In response to these questions:
Are there benefits to learning to write with your non-dominant hand?
Spontaneous change of handedness  

I used myself as an example for spontaneous handedness change. 



Example:

I began as a left hander. I spontaneously changed to a semi-ambidextrous right hander.
Two of my three children are true left handers, the other is a true right hander (their father and his family are all right handed).
My parents and siblings are right handed.
 My maternal grandmother was ambidextrous.



Question:

What are the genetics of handedness?
There appears to be a higher correlation with environmental influences affecting handedness, as opposed to the genetic factors; although there is conclusive genetic evidence, it is not the major contributing factor in determining handedness.

I quote from the link @what provided in the comments.


  Handedness displays a complex inheritance pattern. For example, if
  both parents of a child are left-handed, there is a 26% chance of that
  child also being left-handed.[8] A large study of twins from 25,732
  families by Medland et al. (2006) has indicated that the heritability
  of handedness is roughly 24%.[9] This leaves about three quarters of
  the effect to be explained by environmental factors.
  
  To date, two theoretical single gene models have been proposed to
  explain the patterns of inheritance of handedness, the first by Dr.
  Marian Annett[10] of the University of Leicester and the second by
  Professor Chris McManus[8] of UCL.
  
  Both models propose that there is a variant in a single gene that has
  two alleles. Carriers of one allele are more likely to be
  right-handed, and the other allele does not specify the direction of
  handedness, instead leaving it to chance. They differ on the precise
  effect of the 'right-shift' allele, but both models provide similar
  fits to data on the inheritance of handedness. Oxford University
  psychiatrist Professor Tim Crow has taken the single-gene model one
  step further, and proposed that mutations in the gene PCDH11X were
  responsible for the evolution of handedness, cerebral asymmetry,
  language, susceptibility to schizophrenia, and was the speciation
  event that created Homo sapiens.[11]
  
  Although single-gene models can be fitted to the data, a number of
  genetic linkage studies have been performed, all of which have
  provided evidence for different regions of the genome contributing to
  variation in handedness.[12][13] [14][15] Only one of these studies
  has led to the identification of a specific gene that is proposed to
  contribute to variation in handedness. [16][17]
  
  Medland et al.[18] found a gene that is positively correlated with
  left-handedness in females, and negatively correlated in males. This
  may help to explain why there are more left-handed men than women
  (around 12% in men versus 10% in women globally).3


It is, also, important to define handedness, or types of handedness, and the variability between self-reporting and objective evidence.


  However, genes influencing sidedness remain elusive. We measured
  direction and consistency of hand, foot, and eye preference in 584
  Mexican-Americans from families participating in the San Antonio
  Family Diabetes/Gallbladder Study. Using maximum-likelihood-based
  variance components methods, we estimated weak (.11 ≤ h2≤.17) but
  significant heritability for foot preference, eye preference, several
  hand preferences (writing, drawing, throwing, using scissors, using
  spoon, striking match), and a composite hand preference trait.
  Self-reported handedness was significantly heritable (h2=.57), whereas
  hand preference for opening a box or using a toothbrush or knife was
  not. Many trait pairs had significant genetic correlations, and all
  had significant environmental correlations.


(Heritability and linkage analysis of hand, foot, and eye preference in Mexican Americans  Diane M. Warrena*, Michael Sternb, Ravindranath Duggiralac, Thomas D. Dyerc &amp; Laura Almasyc   DOI:10.1080/13576500600761056)

There is also the concept that handedness is on a continuum and that there is not, necessarily, a definitive left or right handedness, bit rather where the individual sits on the contiuum of cerebral dominance. This study also examines  the genetic modelling versus the environmental factors, and the unreliability of self-reporting. It also, introduces the idea the people may under-report left handedness. This also demonstrates that left handedness is inherited maternally.


  Whereas many assume there is a true incidence of left-handedness, the
  RS theory suggests that degrees of hand preference map onto a
  continuous baseline of asymmetry that can be cut at any point to
  represent observed incidences of left-handedness. The parameters of
  the RS genetic model were derived from findings for speech
  lateralization in aphasics, supporting the argument that the relevant
  genetic locus is “for” cerebral dominance, not handedness. Genetic
  predictions are given for two levels of parental left-handedness (10%
  and 20%). Studies of family handedness distinguishing for sex in both
  generations gave generally good fits where handedness was assessed by
  self-report, but more variable fits for indirect report of relatives'
  handedness. The tendency to find a higher proportion of left-handed
  children born to left-handed mothers than left-handed fathers is not
  likely due to X-linked inheritance, but rather to slightly stronger
  expression of the RS+ gene in females than males, and also
  under-reporting of left-handedness in mothers by right-handed
  children.


(The genetic basis of lateralization Marian Annett dx.doi.org/10.1017/CBO9780511576744.006)

There has been research demonstrating that the LLRTM1 gene contributes to handedness. This gene has also been linked with increased incidence of schizophrenia. An interesting observation, given the historic "demonisation" of left handers. Could this be, because there was a perceivable  increased incidence of "insanity" amongst the left handers? (note, my own theory) 


  Left-right asymmetrical brain function underlies much of human
  cognition, behavior and emotion. Abnormalities of cerebral asymmetry
  are associated with schizophrenia and other neuropsychiatric
  disorders.....    This is the first potential genetic influence on
  human handedness to be identified, and the first putative genetic
  effect on variability in human brain asymmetry. LRRTM1 is a candidate
  gene for involvement in several common neurodevelopmental disorders,
  and may have played a role in human cognitive and behavioral
  evolution.


LRRTM1 on chromosome 2p12 is a maternally suppressed gene that is associated paternally with handedness and schizophrenia. Francks C, et al.



So, given my example, it is not surprising that:


The left handed family members were all on the maternal side.
The incidence of left handedness was low.