from a physical point of view, the alpha particles interact electromagnetically with the nuclei as well as electrons, they interact with each other as they are flying plus there are many experimental considerations that need to be taken into account. When analyzing the problem theoretically, we must make some assumptions to get analytic results. We assume the alpha particles have a constant energy, interact only with the atoms of the gold foil, we assume, furthermore, that the atom consists of a tiny nucleus where the total positive charge is concentrated, the electrons are thousands of times lighter than the alpha particle, and thus will be far more likely to be scattered themselves than scattering the alpha particle, plus they are spread out over a very large volume (and thus the consideration of the pudding model applies to them), we can also assume that the interaction is not continuous, but momentary (like mechanical collisions, since the size of the nuclei and the alpha particles is small and outside the atoms the positive nuclei are screened by the negative electron cloud, so that the alpha particles only interact with the nucleus in a very close vicinity of it) and so on. Using all these assumptions, which are all physically motivated, we arrive at a simple equation that tells us the probability of an alpha particle scattering under a given angle. Then the results of the experiment can be compared to the predictions of our model, and since the agreement was pretty good (considering all the assumption we’ve made) we can be sure that we’ve found something important and use the nucleus model.
Alpha particles are just helium nuclei that have been stripped of their electrons. Sure they have a +2 charge, but it is not enough to eject electrons from the energy shells of gold.
To remove electrons from the outermost shell of one mole gold, 870 KJ/mol of energy is required. On supplying this much energy, one electron is removed from each of the gold atoms.
An alpha particle just can not apply a nuclear force strong enough to completely remove electrons from gold atoms.
But the electrons and the alpha particles must have an interaction because of opposite signs? Such interactions are very weak, and in case of alpha particles, their high velocities don't allow them to have a significant impact on the electron cloud.