This question would probably be a better fit for law.stackexchange.com. With that said, I'll try to answer it from the legal perspective.
Firstly, guidance is not law. Guidance is instead usually (a) a summary of what the author of the guidance considered to be the law at the time of writing, and/or (b) a collection of recommendations which are not legally binding (usually phrased in terms such as you "should" do something, as opposed to you "must" do something). So, while the guidance is a useful starting point particularly for people without legal experience, it can (and does) contain things which are not completely accurate from a legal perspective. With that said, guidance can sometimes be useful in a court setting and I will explain below how this could be relevant for the coronavirus rules.
The legal position differs depending on whether you are in England, Wales, Scotland or Northern Ireland. As you didn't specify which I will answer on the basis of England, but you can find answers for the other regions by looking at the equivalent regulations.
The rules for England are governed by the The Health Protection (Coronavirus, Restrictions) (All Tiers) (England) Regulations 2020 (as amended). The relevant part for our purposes is Schedule 3A (Tier 4 restrictions.
The starting point is paragraph 1(1):
No person who lives in the Tier 4 area may leave or be outside of the
place where they are living without reasonable excuse.
This is expanded upon in paragraph 1(2):
For the purposes of sub-paragraph (1) - the circumstances in which a
person has a reasonable excuse include where one of the exceptions set
out in paragraph 2 applies;
Here we have a very common source of misunderstanding. While paragraph 2 contains a list of exceptions, this is not an exhaustive list. This is clear from the wording of paragraph 1(2) above - circumstances of reasonable excuse include the exceptions but that does not mean there cannot be other reasonable excuses. The purpose of paragraph 2 is to provide a list of scenarios in which you definitely have a reasonable excuse (i.e. you cannot be prosecuted if your facts fall within one of those scenarios).
That leaves open the possibility of other reasonable excuses. Here, you take more of a risk since you do not have the protection of being covered by any of the exceptions. Instead, you would be reliant on how a court would judge the reasonableness of your actions. The word "reasonable" in a court usually refers to what is know as the objective test. This means that it isn't based on whether you thought your actions were reasonable, but rather whether a so-called "reasonable person" would have thought so. This is where the guidance can be legally persuasive. If the guidance suggests that you should or should not do something then, even though it isn't legally binding, it might persuade a court that it was reasonable or not reasonable to do that thing since a "reasonable person" would probably think it was reasonable to follow the guidance.
An approach which may increase the chance that a court would side with you is if your scenario is similar in spirit to the scenarios listed in the exceptions. Your scenario seems serious enough that it potentially could be a reasonable excuse. But as said above, you will always take some risk when doing something which is not explicitly listed as an exception.
Turning back to the exceptions, the exception in Schedule 3A, paragraph 2(7)(e) is probably closest to your case:
[Exception 4 is that it is reasonably necessary for P to leave or be
outside P’s home] to visit a person (“V”) receiving treatment in a
hospital or staying in a hospice or care home, or to accompany V to a
medical appointment and P is a member of V’s household, a close family
member of V, or a friend of V.
Note the words "reasonably necessary". If there is an alternative to you leaving your home, then it is arguably not reasonably necessary for you to do so.
The exception in Schedule 3A, paragraph 2(9) could also be a close match, depending on your mother's prognosis:
Exception 6 is that it is reasonably necessary for P to leave or be
outside P’s home to visit a person (“D”) whom P reasonably believes is
dying, and P is a member of D’s household, a close family member of D,
or a friend of D.
