Probably too far away to be stable, is the way these things usually go, but it isn't so implausible that you couldn't just squeeze it into the realms of plausibility.
I think it is OK to model the binary stars as a single mass, for the purposes of simplifying things a bit. That gives the larger of your two planets a Hill radius of ~2.3 million kilometres. Stable orbits are likely to be within a third of this, so lets say ~765000km.
Tidal locking timescale can be approximated by $$T_{lock} \approx {\omega a^6 I Q \over 3Gm_p^2 k_2 r^5}$$ where $\omega$ is the satellite's rotational rate in radians per second, $a$ is the satellite's orbital semimajor axis, $I$ is the moment of inertia (which is the satellite's moment of inertia factor x the mass of the satellite x the radius of the satellite squared), $Q$ is the dissipation function, $G$ is the gravitational constant, $m_p$ is the mass of the larger world, $k_2$ is the Love number of the satellite and $r$ is the satellite's radius.
That's an unfortunate number of unknowns, some of which (like $Q$ and $k_2$) are not really well known for other planetary bodies. With a bit of handwaving, you can set $Q$ to be 100 (if wikipedia is to be believed) and $k_2$ for your smaller world (again, using wikipedia's suggested approximation) will be something like 0.94. That's a little high for the tidal locking approximation (which wants $k_2 \ll 1$) but we can throw caution to the wind and try it anyway (FWIW, your smaller planet's $k_2$ is about ten times higher than the our own moon). I'll use the approximate moment of inertia factor of the Earth (.33) and use a 24 hour day.
Throwing all those numbers in gets a tidal locking timescale of about 100 million years. That's far too short by the standards of planetary evolution, and it seems very likely that your worlds will be tidally locked to each other long before interesting things could evolve on them. They can't be mover farther apart (increasing the $a$ term which dominates rapidly as distances increase) because their co-orbit is likely to become unstable, and they'll fall out into separate orbits around the central primary.
Now, this is only a very rough approximation, and a lot of handwaving went into the many different unknowns. It is very likely to be out by at least one order of magnitude.
If it is out by two orders of magnitude, then there's room to squeeze in the rotation that you wanted. That seems unlikely to me, but not totally beyond the realms of possibility. If your secondary was spinning much faster initially, for example, it might be possible to have it still spinning in your setting's "present". I'm not sure what a plausible rate of rotation is, but "full rotation in under 3 hours" seems like a stretch for such a big body, though it might be dense enough to survive such a situation intact and would give you at one of the two orders of magnitude you needed (and the second could be handwaved in given the number of wild guesses in the parameters!) Tidal forces would have slowed that earlier dizzying rate to something much more sedate.
