Is a family care plan needed if one spouse is active duty and the other is in the reserves?

Yes, because as long as you both serve in uniform, you can both be deployed (my parents learned this in the gulf war and my mom had to get out of the military entirely)

whether it is required or not, you need to have one in case you both get deployed. Better to have one and not need it than need one and wind up scrambling at the last minute.

As a former duel military couple (active and reserve), I have seen different commands enforce or ignore family care plan requirements. AR 600-20 Chapter 5 (pg 39) states the FCP is for "Mission, readiness, and deployability needs especially as it affects AA, ARNG, and RC single parents, parents with custody pursuant to a court order or separation agreement, and dual military couples with Family members." It does not specify the relationship of the "duel military couple". It does go on to say that ARNG and RC SM are subject to this policy and will implement the FCP during ANY period of absence (Annual Training, Battle Assemblies, and Mobilizations).
If either command is asking for one, get it done. Even if they are not asking you should have a plan in place in the event that you are both called to out of town missions.