Step one ... take a deep breath and relax! You can't help your dog in "Freak out or mode" or in seriously ticked off at this freaking dog mode. As was the case with me ...many years ago. Neither approach is to useful ... trust me on that.
I'm gonna guess that "because" your dog lost his leg and so sorry that happened! But it tugs at your heart ... but took him in and you'd think ...he'd be "grateful??" Forgot that it does not work like that, your dog has forgotten about it and you should to. My Rocky was a foster fail ... and he was a "Wobbly Dog" when I first saw him "Wobble" unto my lawn as a foster ... I cried and I thought to myself "there is a dog that will never find a home! Little did I know ... he already had!
But you know that episode aside ... he was the first Dog that sent me to the ER for stitches (breaking up one of five packs and H/A was to follow) so much for gratitude! But ... lessons learned and it all worked out in the long run.
First step is as you have discovered ... no more toys ... "if" this dog is not under control and right now ... he is not! You have a Cat and a Tiny Dog. Either of those alone is more than enough to send him back to rescue ... if it does not work out so well! But I'm gonna "assume" that is not what you want to happen??
I don't know how long you've had him?? But it does not matter start over and try again ... see the first link here. :
That is not what I did when I got Rocky ... most likely I did what you did when I first got Rocky, here's the food and water there's the couch and the remote ... make yourself comfortable. He was dog three of two and that "laissez-faire" approach ... did not work out so well for me and Gunther ... lesson learned!
He (Rocky" needed more rules/structure and limitations then my "other dogs" once I clearly understood that ... it worked out fine.
The goal ... is gonna be "Self Extinguishing Behaviours." No free roaming in the home in doors he should be in "Place or in his Crate!" He should not be allowed to make "independent" decisions on how he "chooses" to deal with issues!
Train "Place" and no free roaming in the home details and walk him! And a lot of your "issues" will self extinguish.
He really does not sound that bad ... you just have to help him ... "make better choices." I got more if you'd like and Welcome aboard ... sorry it's a bumpy ride so far.