Many sudden infant deaths occur in the days immediately following vaccines. What research have you done on this connection and what advice do you offer parents educating themselves about vaccines?

Red Nose recommends that babies receive the normal program of immunisations at the scheduled ages, both in infancy and beyond.

Red Nose has the following information - (full article & references on Red Nose web site)
No study has demonstrated an increased risk of Sudden Unexpected Death in Infancy (SUDI) with immunisation. Similarly, no study has shown an increase in autism with immunisation

In fact, several case control studies have confirmed the reverse, with SUDI less common in the immunised group compared to those who were not immunised.

Some studies have even confirmed the SUDI rate in the immunised group is nearly half that in the non-immunised group. In South Korea, which has universal immunisation, recent data showed few SUDI or sudden deaths reported in the first 2 years of life.

Recent research has shown no increased risk of SUDI in the 14 days following immunisation or that recently introduced vaccines (e.g. Hib against Haemophilus) are associated with an increased risk of SUDI.

The German SUDI research group showed clearly that immunisation reduces, rather than increases, the risk of SUDI significantly
https://rednose.org.au/article/immunisation