There's ongoing debate about whether SPX and VIX options contain different valuable information (see Bardgett Gourier Leippold (2013) - Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets among recently contributions). I would say this is slightly counterintuitive (VIX index is calculated as a portfolio of SPX vanilla), but at the same time, is the fact that VIX derivatives provide a pure volatility exposure (and traders know it much better than me) that make them conveying a different information, at least concerning volatility dynamics. This said, I would use a consistent model calibrated on both markets. Moreover, in the context of VIX options, there's no Dupire equation (linking VIX option Prices to a VIX implied local volatiliy), but - in some sense parallel - there's an approach called the standalone approach (see Mencìa Sentana (2012) for an update reference), in which one models directly the VIX (without care of the S&P500 market). I would use this If you need a pure pricing machine. But, a structural model as the one I mentioned before is needed to have a perspective of the market as a whole (e.g. estimate risk premia).
To conclude, you could off course even simply interpolate the VIX implied surface as is common practice in SPX context. But I don't think this what you meant.