Firstly, however..er.."wittily" she put it, she is extremely rude and selfish.
I can understand your worries about the mums talking but I think you can diffuse this and show the other mum up to be being unreasonable and selfish, without having to stick the boot in, all with the use of UTTER BEWILDERMENT
Don't email her back yet. Do a bit more subtle digging for information on what has happened.
I would contact the other mum who is now apparently 'hosting' your DS's party and say not sure what's happened but X mum appears to have unilaterally changed your party venue to her house and that you just wanted to contact her to say sorry, not your idea at all, not sure what has gone on but didn't for one moment want her to think this was anything to do with you and that, of course, you will be having party at your house, (and thank her for even entertaining the idea but you'd never be so rude, hope she can take it as a compliment on her house being so nice and spacious! Even have a joke about your house being the house where it doesn't matter so much if the carpet gets ruined because (a) it's got to go sometime; (b) the patterns hide the stains!). Check whether she and her DC can make it, reconfirm details etc.
I suspect that even if nothing overt is said about X mum (and you don't want to get into bitching) the other mum and you will have an implicit understanding that what X mum has done is very odd, to say the least.
If X is the kind of mum to want to be drinking coffee in the kitchen all the time, I shouldn't wonder if this hasn't been noticed by other mums. V tiresome when someone treats other people's houses like a fricking creche. Believe me, if you think the other mums are gossiping about your housekeeping standards or old lady carpet, a lazy mum who expects others to supervise her children or considers herself off duty at others' houses will soon trump that - if it hasn't already.
Then ring round the other mum's, reconfirm date, invite etc.
And when you have done all that, email X mum back to say you've thanked the other mum for the offer but you wouldn't dream of asking someone else to host your DS's party, pretend that you think she is trying to help YOU out by moving venue so thank her for that but it wouldn't be helpful because (a) you've already prepared at your house and (b) you don't want to have to drag over food/games etc to prepare at other mum's house so would actually be much more work for you. Besides which DS is v much excited at thought of party at his house.
X Mum will have to have a neck of brass (which she may well do) to email back to explicitly, clearly, absolutely (no witticisms) say No you have misunderstood. I want you to move your DSs party for MY convenience not yours. In which case you'll be really sorry they can't make it.
Hope it works out, and good luck with the party. Then just enjoy focusing on making party as fun and house as welcoming as possible. There's loads of good threads on here about parties (and easing the pain thereof).
(sorry for length - typing equivalent of verbal diarrhea)