Both of your versions are good and correct, but this version is what I would prefer:
Kannst du dann vielleicht meine Mutter anrufen?
German word order is much more flexible than English word order. The reason is, that in German grammatical functions often are not marked by the position of a part of speech in a sentence, but by the declension.
Der Jäger erschießt den Hasen.
Den Hasen erschießt der Jäger.
Both sentences translate to English "The hunter shoots the rabbit." But in the German sentence you can see, that only "der Jäger" is in nominative case, while "den Hasen" is not, so only "der Jäger" can be the subject who pulls the trigger and therefore "den Hasen" only can be the object that gets killed, and this is independent from the position within the sentence.
If you would do that in English, you would get "The rabbit shoots the hunter", but now you have nothing to identify the hunter as the one who pulls the trigger. Only the position tells you who is who, and when in an English sentence the rabbits appears before the hunter, then the hunter will die, so you can't do this in English.
In German sentences you find this flexible word order also when declension doesn't help to identify the grammatical function, but sometimes it's just the kind of the part of speech itself, that tells you what's its function.
The rules that tell you, what is best practice, what is allowed and accepted, what is allowed but bad style and what is forbidden are complicated, and the average German native speaker is not able to phrase this rules. This is like you would try to explain how you move your legs when you walk. You can do it, but you can't explain.
Resources like the site you linked are helpful. But they are as helpful as a written instruction of how to move your legs. You will only learn if you do it. This means: Use the language. Watch German movies, listen to German podcasts, speak German and write German. You could start with asking your next question here on German Stackexchange in German language.