Hi Moze, firstly I would like to say how handsome Moses is. Definitely a herding breed in there somewhere, possibly sheltie.
Second, I want to reassure you that what you are experiencing is very common with both a herding dog and a rescue dog. Herding breeds are prone to being naturally aloof towards strangers, this can be exacerbated by a difficult upbringing, such as a lack of socialisation or even worse, rough treatment. As you have no knowledge of his past, you cannot know what has caused this, it might even be inherited from parents who had uncertain temperaments.
I have two people shy dogs, Merlin (in my profile pic) and my spaniel Sparrow. Both had parents who were prone to barking at people when they entered the house, so genetics are at play. I have owned them from 8 weeks and socialised them loads, yet that reserve has always remained. Both dogs have improved and are pretty good at agility shows, in fact they are very friendly, but on walks they like to avoid people and have been known to bark at people who try to be too friendly with them. Sparrow has even growled.
They are not happy with visitors coming around. Merlin will bark, then he will settle and even say hello. But Sparrow hides behind the sofa, growling and barking, a very scared pup. This is despite being introduced to a lot of people. She had a traumatic experience when she was around 15 months, requiring emergency surgery. This has left her nervous of men and strangers in general. She is terrified of being taken from me, she won't even go with the trainer she knows and usually loves to demo an exercise at club.
There are lots of things, however, you can do about this and I have slowly improved Sparrow's confidence around strangers, and Merlin has improved enormously.
Be aware that a month is a very short time in terms of a rescue dog. When my brother took on his rescue greyhound last October, we were told it would take 6-8 months for her to settle, bond with us, and for her true personality to come out. Many rescue dogs have no reason to trust people and, especially with sensitive breeds, this can lead them to prefer avoiding people rather than approaching them. It sounds as though Moses has connected with you and has decided you are very important to him. I suspect there were several aspects to why he growled at your mother - surprise at her sudden appearance, fear, and protectiveness towards you. Rescue dogs often attach themselves to a person very intensely, because they have not had that opportunity before.
Angel, my brother's greyhound, has become very attached to me as I look after her during the day. She even tried to prevent my other dogs getting near me by growling, because I was now of such high value to her.
Actually, give yourself a pat on the back for creating such a bond with Moses! He clearly thinks you are very special!
So, how to deal with this? These are the ways I would deal with it, other people will have other suggestions. I have tried these methods and know they work.
1. Create manageable, safe places for Moses. This might be a playpen or a room you can block off with a stairgate. These need to be 'Moses only' zones, places he can be without anyone, bar yourself, reaching him. Equally, while you are working through the problem, having these safe areas means you can put Moses somewhere when your mother is around and you haven't time to train him.
2. Make your mother's arrival a special, but relaxed occasion. Have her bring him a treat, give it to Moses, then utterly ignore him. She should not try to pat him or make eye contact. Equally, when she enters a room where Moses is, she could try greeting him as she enters and giving him a high value treat, so her arrival is something to be looked forward to, not worried about.
3. Play the Look at That game. I love this one! You can use it for when you are walking Moses and he is worrying about other people. It helps if he is conditioned to understand a clicker, but you could also use a marker word such as 'yes'. It should be different to your praise word. When Moses sees a person and looks at them click or say 'yes' before he has a chance to bark/growl. If he is conditioned to the word/click he should look up to you and you can quickly reward him. He may look back towards the think that is worrying him, that's fine, say 'Look' and then instantly yes/click. Basically, you are teaching him to look at the thing that worries him in a calm fashion and be rewarded for it. Very quickly dogs learn that looking at you is more important than the scary thing. In fact, very often they start to ignore what worries them.
I played this game with Sparrow in our obedience class when she became worried over another dog in the next ring. We had never played the game before, but within 30 seconds she was ignoring the dog and focusing completely on me.
4. Incorporate your mum into training games. Start with the 'look at that' game in your living room with your mum sat on the sofa, not making eye contact with Moses. Gradually bring Moses closer and closer to your mum, so he is right next to her when he is offering the 'look'. Don't worry if he stops bothering to look at your mum, that is a good sign and means he has figured out that she is ok to be next to.
Next I would teach him to target something. I use the lids off Pringles tubes as targets. Rub a bit of treat on the lid and when Moses sniffs it click/yes and reward. You can add a cue like 'nose'. As he improves, move the target closer and closer to your mum, eventually have it in her hand. Ultimately, when he is confident with that, she could have a treat in her hand that he takes.
At that stage you could start seeing if Moses will go to her when she gently calls him. Again no eye contact, but say his name, offer the hand with the treat and let him take it. If he runs straight back to you, that is fine. If he hangs around for more treats, that is awesome. Now you can play recall games where he runs between the two of you, and your mum can start offering him gentle praise. The perfect end result would be if your mum could ask Moses to do a sit when he comes to her and then reward.
She shouldn't try to stroke him until his confidence has grown and when she does it should be by stroking under his chin, rather than on top of his head which many dogs find intimidating.
5. Lastly, if you feel Moses is stressed you could try a herbal calming remedy. I don't know what they sell in other countries, but in the UK there is CSJ Calm Down or Yucalm, both of which are safe herbal treatments. You can also put Bach's Rescue Remedy in the water bowl. And there are things such as Adaptil plug-ins or collars. I have used Calm Down and Yucalm at various times with Sparrow, when there is a stressful time occurring. They seem to help.
All that sounds a lot to do, but you can break it down into 1-2 minute sessions 2-3 times a day. My training sessions at home rarely last more than 5 minutes. You will be amazed at how much dogs can learn in such short sessions and how fast they progress.
With management and patience you will get through this. I remember the first few months with Angel were filled with little episodes. She would growl at the other dogs when they came near her bed (she had never had her own bed before). She would growl/snap at dogs when they approached her in the park. She growled at my dad once when he tried to push her off the sofa (I had words with him about that). And, more recently, my brother had friends round for a birthday BBQ and Angel went and hid in a bedroom. One of his friends insisted on seeing Angel and when he tried to stroke her she growled and snapped. Had I been there I would never have let things get that far.
You can overcome this and help Moses to be a happy, confident dog. He may always be people shy, but that is not a problem. Just don't allow strangers to force themselves on him. Good luck with your gorgeous boy.