Is differential equation modelling in molecular genetics useful?
Are differential equation models useful to geneticists and biologists?


Well yeah, of course they are. Look up Alan Turing and "The chemical basis of morphogenesis", or look up "differential equations and gene regulatory networks" But folks have to specialize, and not every department studies every aspect of a field. You may just have ended up in a department where nobody is studying an aspect of genetics that can be well modeled by differential equations. At lot of molecular genetics is still figuring out the coarse grained phenomenology of the genome, like "How does a cell figure out which copy of the X chromosome gets condensed into a Barr body?" A lot of these problems involve picking out subtle signals from noisy data, thus the interest in statistics and machine learning.

If diff. eqns. are the passion of your life, you might have to look 'next door', to departments studying biochemistry and population genetics, both of which do huge amounts of modeling using differential equations. There are also applications of differential equations to molecular genetic methods like QPCR and next generation sequencing, but you'll either have to sell your mentor on the topic, or move to a different department.

On the other hand, if it's just a matter of diff. eq. being your undergrad emphasis, you may want to find a biological problem that interests you, branch out beyond diff. eq., and use your general mathematical maturity to pick up the relevant mathematical tools: say statistics, optimization, or dynamic programming.