I received two budgies last Christmas. This is my first time owning birds.
My mum, who bought me them, also gave me a parakeet info book, and I've been taking my info from there.
Dawn is a young female and Dusk is an older male.
I know I have to be quiet around them and there shouldn't be any loud noises, but that's near impossible because I have two younger brothers who tussle and yell constantly, two big dogs with an addiction to barking and being in my room, and other family members (who I love) who are beginning to lose patience with my slow and steady approach to taming them. (Insisting they can help tame them, going fast right up to the cage, sticking hand in, saying I'm just afraid, etc etc)
They have barely, if at all, begun to trust me with changing their food and water. If I stay there for more than 10 seconds, bang the food/water dishes even slightly, etc, they get all fidgety and tense up, never taking their eyes off me. A few times, I managed to somehow freak them out so much they panicked and flew around wildly. I've tried a few times holding out individual pieces of millet to them vaguely around the same time each day, but they'll fidget, then go perfectly still after about 4 minutes and close their eyes.
I'd really appreciate any help with this, I don't want my birds to bang their heads too hard, or my family members scare them into another two-three months of training.
I would suggest you speak with your parents and ask to move the budgies into a different room where you will be the only one to interact with them. Otherwise, with people walking up and sticking their hands in the cage, the budgies are never going to learn to trust you and will always be afraid.
Since you have dogs in the home, please be sure you read this thread:
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Budgies need to be in a stable and stress free environment to truly thrive and be happy. If your family has a difficult time in understanding this and is not willing to learn on the best practices for budgie keeping and making the needed compromises, then rehoming your budgies to someone experienced who will provide everything your budgies need to have a happy and fulfilling life would be the best option.
To have your budgies in the type of environment you have described for at least two whole years is to me not at all acceptable as that can have long-term consequences on their mental health not to mention their physical health too, if one of your dogs happens to give in to their natural instincts and attack your budgies. Even while on the cage, a budgie can still get injured and die from a dog attack.
The "taming" approach made by your family is also not the right one and your budgies can develop a trauma for hands/people etc and rehabilitation after two years of being exposed to that kind of environment can be quite a long and difficult process even for the most experienced of pet bird owners with the know-how on rehabilitation.
Unfortunately, it seems now is not the right time for you to have budgies or pet birds of any kind and screening a potential good family for them would be the right way to proceed.
I'm sorry to hear that things have not been going well with your family members and your budgies. Although I know you love your budgies and this isn't what you want to hear, it is unhealthy for them to be constantly in fear and under stress simply because your family doesn't want to respect or understand the conditions needed to get them used to you and their home.
In time, once you have your own space, I agree that it would be a better time then to have your own budgies
The dogs should never be in the same room with the budgies when the budgies are out of the cage. Once the budgies have become used to the environment and are more settled, it may be possible to allow the dogs in the same room ONLY when completely supervised and if the dogs are very well-behaved.
You need to be able to tame and bond with your budgies yourself before adding other people into the mix given the way your family has interacted with them thus far.
Once the budgies are comfortable with you alone.
You can introduce them to family members if the family member follows the rules of moving slowly, talking to the budgies very calmly and never tries to grab the budgies or force them to do anything.
However, at this point, you need to take things one step at a time and always work only at your budgies' pace.
If you are unable to do these things for your budgies, then it is in their best interest for you to rehome them to someone who can give them the love, care and attention they deserve in a stable and well-adjusted environment.
Ideally you'll have your own bedroom and the budgies will be housed there. That arrangement would probably give you the most control over who has access to the birds - obviously your family would have to respect your control within that space, this will be more likely if you do the same with your younger brothers (e.g. Knocking on their doors before entering).
I advise that you stick a 'Please keep this door shut' notice on both sides of your/the budgie's room as a reminder to other family members who may still pop in when you're not there. Decide on and make sure that everyone is aware of a sign that you'll use when the budgie's cage is open (e.g. A written door sign that you put out or a cloth tied onto the door handle).
Both you and your family need to be aware that this taming process is unlikely to happen quickly. Your birds were very skittish from the start, they've had that wariness confirmed by your dogs and impatient family members and having more than one bird lessens their need to bond with you. Don't lose heart, it's not impossible but it's likely to be very slow.