I don't know where you are (apart from somewhere that prices in Euros) but do you have local phone repair/refurbished phone shops? How old was the broken phone? Is it possible it could be repaired/replaced for less than 300 Euros?
In choosing a replacement, what does your younger daughter need? It should be a reasonable replacement in having the functions she needs, and presumably a smart phone, but that may not require spending exactly the same amount of money.
I know that what was available when my dad bought DS1 a phone was different when he did the same thing for DS2, probably under 2 years later (they are 21 months apart and I think DS2 was closer to turning 13 or was just 13, whereas DS1 was a few months off his birthday). DS1 had to get his fixed a couple of times, including a broken screen, but then his aunt (my sister) very kindly offered to get him a replacement last time it was damaged, and his first one was probably slightly over 3 years old. All 3 phones were Samsung, but different models. I believe DS1's phones were compatible enough for him to switch his SIM card.
I do think that your DD1 should be asked to contribute the money she has at the moment, and maybe make some instalment payments, or wait on the hair colour appointment, and perhaps save towards that herself
I'd avoid enforced phone swaps.
What would DD1 expect if her sister or a frenemy etc had broken her phone?
I think you need to talk to your DH more about how you intervene, and that he needs to tune into what's happening (including the hearing aids). Would he be able to take DD2 to a phone shop, or help her research what's available.
What options do they have for being in a separate space in the house, rather than in the same room arguing?