To successfully contest your MIL's will, her son would need to prove that
(a) she didn't have the mental capacity to make a valid will ; or
(b) that someone exerted undue influence over her when she was making her will (either under the provisions of 'undue influence' or 'facility and circumvention') ; or
(c) that a beneficiary had benefited from fraud.
https://www.rocketlawyer.com/gb/en/quick-guides/contesting-a-will-in-scotland
I can see nothing in your post which would present him with a valid reason.
In England and Wales it's possible for a child of the deceased to challenge the provisions of a will on the grounds that the will failed to 'make reasonable financial provision' for them. (NB: That's NOT the same as a child of the deceased having an AUTOMATIC right to benefit from the estate of their parent. They have to show that there's a valid reason why they should have been included in the will or have had greater entitlement under it). The relevant legislation does NOT apply in Scotland though, so if the son is relying upon it, he's clearly wasting his time.
However, under Scottish law the son DOES have an AUTOMATIC right to receive part of his mother's
moveable estate. (Nothing his mother writes in her will can change that). Assuming that your MIL hasn't got a surviving spouse or civil partner, that means that the three children have an AUTOMATIC right to share half of your MIL's MOVEABLE estate between them. So the son would end up with ONE SIXTH of the MOVEABLE estate.
'Moveable' estate though includes only things such as money, shares, cars, furniture and jewellery. It does NOT include 'heritable property' (such as land or houses).
https://www.redstonewills.com/news/item/what-are-my-legal-rights-in-scotland
So, even if your MIL hadn't signed the house over to your husband, there would appear to be no way that he son could make a claim upon it. As she's already assigned title to the property to your husband though, the house won't form part of her estate anyway so the chances of the son getting hold of any part of it after her death would seem to be even less (if that's actually possible).