I am curious as to why you are not approaching this problem using a point pattern analysis? It is apparent that you are after a multiscale integration but, not clear as to what end or what type of supported inference would be made. The type of standardization that your are attempting is hinting that a PPA would be a more supported methodology.

Depending on your hypothesis, I would highly recommend taking a look at the Geits-Ord or Ripley's-K statistic(s). If you have covariates there are correlogram methods implementing the partial Mantel test, which if permuted, support exploratory analysis. Another option for a marked point process would be the family of scan statistics, which can be specified using assumed point process distributions (ie., Poisson, Gaussian, Binomial) and as a multiscale model. All of these methods provide a spatially lagged (multiscale) evaluation of the spatial process and avoid many of the issues associated with kernel density estimates, which is never really considered a supported inferential method. For a robust inference you could formalize a point process model, in a hierarchical Bayesian framework (MCMC), using the estimated intensity function.

Now, if I have misunderstood and you, in fact, want to integrate the volume of two kernel density estimates you could follow one of the methodologies presented in Hurlbert (1978) that provides mathematical definitions for integrating niche volume overlap. The equations are relevant to any volume integration and the paper is available on JSTOR.

Hurlbert, S.H., (1978) The Measurement of Niche Overlap and Some Relatives. Ecology 59(1):67-77

I am curious as to why you are not approaching this problem using a point pattern analysis? It is apparent that you are after a multiscale comparision but, it is not clear as to what end or what type of supported inference would be made. The type of standardization that your are attempting is hinting that a PPA would be a more supported methodology.

Depending on your hypothesis, I would highly recommend taking a look at the Geits-Ord or Ripley's-K statistic(s). If you have covariates there are correlogram methods implementing the partial Mantel test, which if permuted, support exploratory analysis. Another option for a marked point process would be the family of scan statistics, which can be specified using assumed point process distributions (ie., Poisson, Gaussian, Binomial) and as a multiscale model. All of these methods provide a spatially lagged (multiscale) evaluation of the spatial process and avoid many of the issues associated with kernel density estimates, which is never really considered a supported inferential method. For a robust inference you could formalize a point process model, in a hierarchical Bayesian framework (MCMC), using the estimated intensity function.

Now, if I have misunderstood and you, in fact, want to integrate the volume of two kernel density estimates you could follow one of the methodologies presented in Hurlbert (1978) that provides mathematical definitions for integrating niche volume overlap. The equations are relevant to any volume integration and the paper is available on JSTOR.

Hurlbert, S.H., (1978) The Measurement of Niche Overlap and Some Relatives. Ecology 59(1):67-77