= Solution
Let $s$ index compatible parental phases in family 2, with fixed prior conditional weights $\pi_s$. For a given phase, let $r_s$ be the recombinant count and $m_s$ the informative-transmission count, absorbing any fixed <genotype> factors into $C_s$. The appropriate <pedigree likelihood> is
$$
\boxed{L_2(\theta)=\sum_s\pi_s C_s\theta^{r_s}(1-\theta)^{m_s-r_s}.}
$$
This is <phase averaging in a linkage likelihood>; maximizing over a phase after observing the offspring would not be the same <likelihood>. In the common special case of two equally likely phases that exchange recombinant and nonrecombinant labels across $m_2$ transmissions, it reduces, up to a constant, to
$$
\tfrac12\{\theta^r(1-\theta)^{m_2-r}+\theta^{m_2-r}(1-\theta)^r\}.
$$
The constrained <maximum-likelihood estimate> compares all stationary points and endpoints on $[0,1/2]$.
\b[The actual phase set, weights, counts and numerical maximum for family 2 cannot be determined without its missing pedigree.] The special two-phase expression is a conditional example, not an assertion about this unidentified family.
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