If she's poisonous then you should save yourself the trouble of arranging access. I cut contact with my own parents (both now deceased) and have absolutely no regrets.
However there's definitely another side to consider (not to do with your in laws). Would your own parents or siblings have contact or a relationship with your child? I ask because my family went through an unbelievably sad situation. My DBIL died very suddenly. He had three sons, two from his first marriage and one from his second (DN). We knew the first two DS very well, and DN had visited with his parents as a small child.
DSIL died within two years of DBIL due to an accident. DN was very early 20s and had very little contact with either side of their family.
The situation needs to be considered because no one from either side had a close relationship with this lovely young man - not because of infighting, but because we all lived in different places and he hadn't developed roots with us.
It's a few years since this happened but at the time this lovely young man didn't feel connected to any of us, so no matter how many messages we sent it didn't really mean much to him. He was never rude to us but the feeling of 'family' wasn't there for him, and we realised too late how it's important to allow your children to grow roots with other people who will love them, be there for them and have their best interests at heart. He's happy now though, has a lovely partner, and has moved on with this life.
I read so many things on Mumsnet about excluding relatives for sometimes imagined slights or disagreements, but I really do think that we should all think about the worst that can happen - what if we're not here - who can our child turn to? Please ensure there is someone there who your child trusts and will love them and care for them.
Both my DBIL and DSIS were lovely and kind peopIe who we still love and miss to this day, but they didn't think about this scenario. I still think your IL are arseholes though.