Hello I know you did what you thought was best at the time so try not to beat yourself up over it. I know rescue centres can be tiring as many insist on a home visit etc and thats why many people prefer to go private BUT they know about the cats/kittens they have and so can advise you whether they are cat / dog friendly beforehand as many arent.

However I think the best thing you can do is take them to a local shelter as its also not fair on your resident kitty and its obviously quite stressful to yourself.

Kittens usually dont stay in those places long, some even take the mother as the kitten is still dependant of her. Instead of trying to rehome her yourself and hoping for a good outcome I would seriously think of taking them both asap.

The good rescue centres will make sure whoever takes them is aware of the mums resistance to other pets and therefore make sure the new home is suitable and they will be looked after.

I know its hard but its the safest thing to do, good luck.