You can, but you'll need to educate yourself and do a fair amount of work. The benefits are that you will be in complete control of your case and will be able to make informed decisions as to how to proceed as events unfold. The disadvantages are that the stakes are high (especially in a custody case) and minor mistakes on your part may have long-lasting negative consequences. In general, we feel that Family Court is not a good place to be without competent legal representation.
With this in mind, if you want (or need) to act as your own attorney (acting 'pro se'), there are resources to assist you: