A phase detector and a mixer are similar but not the same animals.
It isn't clear what kind of signal you are trying to recover, as shown, the VCO mixes with the IF down to DC or at least less than 20KHz so you have an AM receiver with poor image rejection. I suspect what you are trying to do is accurately tune the VCO to pick out one signal from the 90 - 110MHz range. The best way to do that is with a PLL, the VCO isn't tuned from the LPF as your schematic shows, it does come from a filter (the 'loop' filter) but that is fed from a phase comparator. One side of the phase comparator is a reference frequency which you choose to be the smallest tuning step you need, the other side is the VCO output through a frequency divider. The VCO then tunes to the reference frequency multiplied by the division ratio and it is as stable as the reference.
I'm not sure what would really happen if you tried the existing design, the VCO would be modulated by the recovered signal so I suspect a rather random oscillation would occur.
Brian.