Difficult toddler coming to DD's first birthday party - advice on handling it?

[MedicalEd]

One of my best friend's DS, nearly 2 will be coming to the party with her DD 3mo.
The boy has no boundaries and both parents seem to think it is funny when he takes toys off older children and makes them cry but to be fair they wrestle with him when he comes to take toys off my (rather delicate and unsteady) DD.
But he is a bit of a bully and is allowed to play with anything he wants (his father said he'd have to pay for our laptop if he broke it when he pulled it off the table instead of telling him not to grab it...)
I hestitated in inviting them at all but have done now so need to know how to deal with it.
There will be 6x 1 year olds, the baby, the toddler and an older girl who I think is about 4 plus all the parents.
Any suggestions for keeping the peace/avoiding injuries and not falling out with parents?
Am leaning that the politics of children's parties are worse than for grown-ups!

Keep them busy. Have party bags so that there is an end to the party and write a list if what you are going to do at the party to keep things moving so that the dc are having a lovely time doing the things they are supposed to he doing.

Try to avoid 'splinter groups' disappearing off upstairs or whatever.

Thanks Savoy, they are mostly all tiny so no splitting up and running away.
We have a baby sensory type class teacher doing a bit and then some snacks and cake time.
What's more of a worry is how to handle parents if the toddler grabs/hits/pushes over a tiny one if toddler parents don't attempt to stop it.
I am just as likely to blurt out something rude if he does it to my DD, let alone the parents of other DCs as they won't know toddler parents.