I'm glad that you're starting to heal from this and starting to forgive yourself, because you are definitely allowed to forgive yourself, as I said already, your birds loved you, they lived a good, loving life, and they have already forgiven you...
****So you said that you've already purchased a new bird or birds? If that is what you needed to do to allow yourself to heal and move on, then good for you...
Can I give you a little piece of advice, or a tip for your future with your new birds? It's wonderful that you have a balcony/porch/deck or whatever place it is outside of your house/apartment that you can put your bird's cage when it's nice outside, most of us don't have that luxury, at least not all year-round due to the late fall/winter/early spring weather, and birds love to be outside...
That being said, there are a few things that you have be safe about to protect them when they are outside by themselves, without a person watching them. Even though they are in a cage, it is still possible for certain predators to get to them...If you're on the ground-floor, then all types of animals can get to them, especially cats and whatever wild animals you have around; if you're up on a higher level/story of your building/house then the ground animals can't get to them, but larger, predatory birds can, like hawks, raptors, eagles, etc. Even large crows and ravens can get to them...and they can grab them through the cage bars...So you have to be careful about that...If the balcony area that you put them on is screened-in, then that eliminates this issue...
****As far as the sun/heat goes, I'm sure you've already figured this out, but in the case of your two LoveBirds that passed away, yes direct-sunlight can kill them, so it's always important to put their cage in a spot that is partly in the shade, and partly in the sun...HOWEVER, please don't EVER put any type of cover over your bird's cage when it is outside in the sun! The cover is no-doubt the reason that your Love Birds passed-away, as any type of cover over their cage is going to heat their cage up and then trap-in that heat, and no breeze can get through either...So I would completely and totally eliminate putting any type of cover over the bird's cage at all if they are outside. Period. That way, even if they do happen to be left outside for too long in the direct sunlight, which can still hurt them if left for too long, they have a much better chance of surviving without a cover over them. I'd speak to your mother/family and let them know that from now on, no one is to EVER put any type of cover on the bird's cage when it is outside. Period.
I hope you aren't offended at me saying this to you, but this is something very small that can make all the difference in the world to the health and well-being of your birds, and I wanted to make certain that you realize that it was the cover over their cage that trapped-in all the heat, so that you and your family don't make the same mistake again...
Accidents happen, and there are always going to be times when someone forgets to do things, like bring the birds inside from the balcony. It happens to everyone, and anyone who denies that these things happen to them is lying, lol...But anything that you can do to help whenever these little mistakes occur is great, like putting in little "safety-back-ups", as no one is ever perfect, and no one can eliminate all mistakes and accidental forgetfulness. So making certain that no one ever puts any type of cover over the bird cage when it's outside is the best little "safety-back-up" that you can put in place for this particular situation...
I wish you and your family all the best, and good luck with your new bird or birds...I hope that you're learning to forgive yourself, and also your mom, as I'm sure that she is blaming herself as well. I could sit here and type for 24 hours straight and not even put down a fraction of the mistakes that I've made with my birds, my dogs, my Bearded Dragons, etc. But I always say that as long as I never make the same mistake over and over again, as long as I learn from it and move forward from it, that it's not really a "mistake" at all, but rather a just me "educating myself"...
