From what I understand, you should give first dibs, so to speak, on everything to the first/original dog (mum), this should control any potential fighting over "pack hierarchy". You (and any humans) are at the top, mum dog is next, then son. So mum should meal first, first pats/cuddles, best stuff first - no need to neglect younger dog, but it just makes older dog feel secure and newer dog will (hopefully) just slip into his new place in the pack.
This is one way to go about it and it has worked for me. Gook luck!
Editing to add... dogs (though not all) love to rough house, and you will probably be pretty sure if they have a serious tiff. My old girl and my brothers dog bark and growl and wrestle, but their body language remains relaxed. When Fenria (old girl) has had enough she lets Odin know and he backs off. And she is half his size (red cattle dog vs Irish wolfhound x ridgeback)!
Maybe you could check out some books from the local library to familiarize yourself with some images of doggy behaviour and body language? Might make you feel more at ease and/or put your worries to rest.