OP I am sorry for the loss of your mum, I extend my sympathies to you and your family and hope you have support at this time too.
As for your brother I think before you say yes or no to him a few things will need to be put in order;
-Why is he leaving your other brothers home? Being kicked out due to behaviour or just feels his will fare better in your home?
-Does he have a solid plan for what he would like to do going forward, college, training or job prospects? An actual plan, as in he has followed up support/info rather than a vague notion of being or doing something.
-How long can you afford to provide for him financially, as realistically it will take time to get himself into training, or a job, can your family take the financial impact of that time supporting him.
-How will him moving in affect the rest of your household? Will he have his own room or will he be sharing with one your DC, or will the DC now share a room to provide space for your DB?
-What is his plan to contribute to your household if he does move in? Helping with childcare, school run, cooking, cleaning, whatever. You do not want a situation where he moves in and acts like another child that you have to care for.
-Is he willing to follow house rules, no parties, drinking or friends around at all hours, basically any behaviours that causes disruption to the routine you have for DC.
-Is there an older relative like aunt, uncle, grandparents that can provide guidance to him, someone that can have a firm talk if needed?
I think before you make any type of decision that you and both DB need to meet and discuss all these things before going forward, it is easy to say "of course move in" but without boundaries and a plan to set him on a solid path for the future it could do more harm than good and I type that as someone who lost their mother at 12 with no dad around and had to move about from relation to relation until old enough to live on my own, it was a horrible time having no real place to call home, no certainty and I felt very unloved and unwanted. Looking back what I needed was someone to have boundaries and be firm so I knew what was expected of me and that I could rely on someone. Being left to float about was harmful to me.
I wish you all the very best.