I'm usually all for child free weddings if that's what B & G want etc., but almost every thread I've read on the topic makes an exception for newborn babies (if said baby's parents are wanted as guests) because it's generally recognised they're highly dependent, can't (easily) be left with someone else, don't run about or have tantrums and are therefore a special case.
In this case, there are a number of other small children there, including another baby, and the baby's parents are close relatives and are each playing a significant part in the proceedings (though OP, in all honesty, I think you've taken too much on by being a BM).
The ONLY explanation therefore as to why you've been 'told' your baby isn't welcome is that s/he will take the shine off their small baby - who, at 2.5 months will of course still be incredibly cute and someone most guests will be oohing and aahing over. I wouldn't mind betting though that either the B or G, or both, feel that your newborn will 'trump' theirs in terms of cuteness and be the 'star of the show'. Either that - or the bride is spoilt and silly enough to think your baby will take attention away from her (but can't deposit her own baby anywhere else as all close relatives will be attending).
Whatever the truth it is, given the circumstances of other kids being there, and your baby being no 'trouble' at all (compared say to toddlers running amok) incredibly rude and hurtful to suggest this. I'm sure some sort of jealousy and/or wanting to be centre of attention (either bride and/or her baby) is at the bottom of it. Which is pretty pathetic.