How is the rate of gluconeogenesis controlled in the cell?
In mammals gluconeogenesis occurs primarily in the liver (together with the kidney to a much smaller extent). When the blood glucose concentration falls, it is the role of the liver to generate glucose for other tissues that are dependent upon it.

Hormones play a key role in this. If one considers the decrease in blood glucose concentration during starvation, this is signalled by a decrease in the concentration of insulin and an increases in the concentration of glucagon. These have differentials effect on the uptake of glucose by different tissues, depending on whether they have receptors for the hormones and the consequences within the tissues, and mass action effects of metabolites will certainly influence whether glycolysis or gluconeogenesis occurs in liver.

However, you are correct in your concern that there must be a way to prevent the futile cycling of intermediates through the different reactions of the three steps that differ between glycolysis and gluconeogenesis. The short answer to how this is accomplished is that the concentrations of various metabolic intermediates change during starvation/feeding, and that these intermediates are allosteric regulators of the reactions, switching one off and the other on. This is described in the section on Regulation of Gluconeogenesis, in Berg et al. (available on-line), from which I reproduce the  diagram below (Fig. 16.30).



Although this diagram illustrates the principle, a few words of caution about the detail are in order. First, the edition of the book this comes from is 15 years old. Second, it is not clear that all the regulatory molecules are effective in liver — some of the work may relate to bacteria. Third, much of the evidence is from studies with purified enzymes. Although it can be shown that an enzyme can be regulated by a particular effector in these conditions, it is different matter to establish that this occurs in a particular physiological condition. Thus, you will need to consult more recent and specialized sources if you are interested in particular details.