You keep using drama llama adjectives, cruel, terrible, exclusion, bullying. You made the bizarre claim that you are "worried this will ruin their self esteem" What utter rubbish, learning to cope with rejection (which you obviously have not) is an absolutely normal part of life, and frankly your kid wouldn't know about it unless you were harping on about it.
The entire conversation should have been "I texted her mum to ask a couple of times, haven't heard back, sorry love"
Your whole attitude to this other persons's child and demands to force her to let you into her life are overwrought, controlling, fixated and over emotional.
You have repeatedly tried to pretend this woman is trying to split your kids up, when she is doing nothing of the sort, she just wants to invite whomever she pleases to her own home.
You have also pretended that children playing together in school and you not controlling and demanding access to other people's homes is exclusion.
Additionally you have made the strange claim that this woman not allowing you to force your way into her home is bad for her child, when it's clear that her child has a great social life, your child is not just involved in it.
And then you made up a weird scenario about children being dragged into school crying because their mothers occasionally refuse play dates with women or children they don't like.
If you walk around spouting such over dramatic attitudes to everything, that will be another good reason this woman avoids you, apart from your lack of self awareness, determination to ignore boundaries and fixation on her child.