Certainly you, the client, have the right to be present at the other depositions in your case. It is, after all, your case. And you can be useful in taking notes and, during breaks, alerting me, or whoever is your attorney, to errors, omissions, new questions etc. that the testimony raises. This can be very useful.
But….. But you being there adds an unpredictable variable to the proceedings. I don’t know how the other side will react, whether they will get more (or less) emotional on seeing you. I don’t know how you will react on seeing the other side and hearing the other side’s story. Clearly, your self-control and ability to play poker will be critical. If you, the client, are the sort who will interrupt every three questions, derail my train of thought, etc., then you probably shouldn’t attend.