Hi retor - welcome to Purrs to you and your extended cat family.
It's a tricky situation when relationships break up
but great to learn that you and your new partner are contemplating moving in together.
It's a huge credit to you that you're considering the problem of integrating your two families in advance, and Charlie sounds adorable
(We lost our elderly dog in February and I really miss having a dog around the place - especially as Tess was a real character, bless her)
I think the success or otherwise of introductions in these circumstances will depend on a number of things, but two of which will be uppermost - the cat's stress levels, and the tolerance levels of you and your partner.
Dogs that are friendly with cats will generally integrate well, but the cats are a different matter. Indoor cats are more prone to stress if they're in multi-cat households (which is not to say they can't get along, just that it can create problems dependent on the nature of the cats sharing the space). Most cats like to have their own "spaces" to hang out and call their own. They like different "levels" too - such as cat platforms (or handy spaces on bookshelves/tops of wardrobes etc) Vicky Halls generally recommends that you have a litter tray per cat, plus a spare. If you haven't already, this may be something you would want to try as an initial measure to see if it eases the inappropriate peeing/pooing any.
If one or more of your cats are already exhibiting signs of stress (ie cystitis and soiling in the house other than in litter trays provided) then this may be made worse by the addition of one or more new stresss related factors. Not least of these will be getting used to a potential change of surroundings if you move, the addition of your partner full-time and the addition of a dog, so effectively the cats could have three new things to potentially unsettle them.
The house move - whilst a possible negative - also has positives - if there's a possibility of safe outside access for the cats, then this could help them to feel they have more spaces to call their own, and if you don't have different levels in the current house where the cats can bag a space for themselves, having a new outdoor space may be somewhere you can create these for them. If there was also somewhere the cats could retreat to where they're out of the way of Charlie and people if they want to be, that would help to give them a feeling of safety. A run could be an ideal compromise, with access to the house. and an outside shelter like a shed, with sleeping spaces for daytime snoozing The chances of Charlie "bothering" them in their safe space would be minial, and Charlie would quickly get used to having the cats about, is my guess. After a while I doubt he'd bother them much (although most good natured dogs enjoy a snuggle with a cat if they get the chance)
It might be an idea initially to introduce Charlie to the cats by bringing home with you something that will hold Charlie's scent, such as a blanket. Let them get used to that before they meet Charlie. Then you could try introducing Charlie to the cats in their usual group in their own home, keeping him on the lead, and by your side - you could aim for fifteen minutes to begin with, gradually increasing the length of time he's there, so long as the cats don't react too badly. Make sure to be with them throughout, and don't make any outward show of anything being any different to usual. If Charlie is happy to sit or lie down next to you and your partner, whilst on his lead, then the cats get a chance to get used to the smell and the sounds of him first - they may just view him from afar - an open door or a staircase. They then have a chance to get away to another room if they feel threatened. Let the cats set the pace. If this goes well, then you can try letting Charlie off his lead, and making sure the cats still have an ability to leave the room or access a higher place if they take fright, or just feel safer viewing him from a distance.
It's good that you have the feliway, but you may need to buy a couple more. Above all, introductions will take time and patience, and are most likely to be unsuccessful from the cats point of view. I would be prepared for problems with the cat who has cystitis. She's most likely to react, although potentially all of them may, and it may be the case that ultimately the amalgamation of the families will only be partially successful. If you arm yourself for the worst, and hope for the best then you stand less chance of being disappointed.
There are many Purrs members who successfully combine dog and cat ownership (and we were one such hosuehold) but a lot depends on when and how the combinations are introduced and the personalities involved. Am sure there will be others who will be able to make suggestions too.
Sometimes, sadly, there will always be winners and losers, and then it's a case of having to decide what is best for the welfare of a pet who cannot comfortably make the transition. In those circumstances then it may be kinder to look to rehome through a responsible organisation, although I know all of us would agree this is a last resort, as its so very hard when you love all of your companions equally. Whether they have foibles and quirks and tendencies, we still love them, and the main thing is, you've already shown your level of commitment and that you would very much like the best for all of your cats and for Charlie and your partner too.
I hope that the intooductions go well if you decide to attempt it, and that you can all end up living happily together as a family.
Doyou have any piccies of your cats and of Charlie? If so, we'd love to see them. Hope you find lots of useful info on the forum.