Hi Matthew,
It sounds like you've had quite a scare.
First let me say that there are 'good' angels and 'bad' angels. The 'good' ones are those who are obedient to God and will present themselves to a person only if he gives the order to do so. However the 'bad' ones are those who were disobedient to God and are allowed to torment humans. Remember the story about the man who hung out in the graves? Jesus called them 'unclean spirits'.
I do believe you, especially when you said your dogs could see them. I used to have a Dalmatian that at night time when we were in bed with the lights still on (I like to read in bed to help me to sleep) She would sometimes get up and stare up at the ceiling, over by the wall. At first when I saw her do this I thought maybe a spider was up there and had caught her attention, but nothing was there. She never growled, or barked, just watched for a few minutes and then would lay back down. After awhile I figured that it might possibly be a 'guardian angel' and somehow it had done some kind of movement that she could actually see.
This happened many many times, usually at night as we got ready to sleep, one time I even saw her stand up on the bed and look towards the ceiling and wag her tale a bit, almost like she saw and heard something 'good' that made her happy and or feeling safe. I don't know but afterwards she would lay down very contented like there were no worries and went to sleep.
At the same time I had this dog my second grandson was born. When we were visiting my son told me about my first grandson pointing up at the fluorescent light in the kitchen a couple of times and saying 'ghost', I think he was able to see an angel as well.
I believe that animals and small children are able to see into that 'dimension' but we can't.
As far as your other questions, I do believe they are allowed up to a certain point to come after you, but only if you have invited them. You may say that you haven't but they can be 'invited' various ways, through, TV shows, movies, Videos games, occult practices and more. You need to repent, meaning turn away from anything like that and close up that door. Your prayers will be heard by God for your protection and your families but you need to pray and ask God to show you how they 'got in' in the first place so you can 'slam that door'.
We were given free will and just as we are told to invite Jesus into our heart, we also can invite 'others' neither can come in uninvited.
I will keep you in my prayers and pray you have a peaceful day.
Paul was aware of this 'other' world and said that (Ephesians 6:12 )
12 For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places.