Elderly rescue cat problems

[Aloneandnowwhat]

I rehomed a cat from a rescue centre 6 months ago, he's a 16 year old male found as a stray. He is always pretty friendly towards me.
These are the problems: I have two spaniels, the cat will not tolerate them at all and basically lives upstairs with the dogs downstairs - baby gate on top of stairs. When they all meet at this baby gate it's like world war 3!
Secondly, the cat has gone to bite my toddler twice now, both times toddler hasn't done anything to cause this, has just gone to touch cat possibly too quickly.
So, any ideas on what I should do? The cat has had six months to get used to the dogs already so that will never happen, it's a shame for the dogs who I've had for 9 years since puppies. I can't tolerate the biting, not when it's totally uncalled for.
Is this cat unsuitable for our home set up? I'm reluctant to give up on him but feel like I've given him a fair crack of the whip and nothing's improving.

Oh, forgot to say, you should find that confidence and interactions then progress.

...progress naturally. (sorry)

I'll try that with ds thanks. I think because he's had pets since birth he's just too confident and doesn't realise they have boundaries. I do tell him to be careful and gentle which he usually is.
Does anyone have any ideas on how to integrate the dogs with the cat, I feel guilty on them being banished downstairs when they've done nothing wrong. There are places the cat can climb on to keep out of the way so could I just open the baby gate and allow everyone to roam?

I've never allowed dogs upstairs and they just accept that (once they've got it which isn't usually long) as one of the rules of the house. I really wouldn't worry about it.

(Neither do they seem to care that the cats may be allowed to do things/go places they can't. I think they know, instinctively, who is boss in any house.)