I For "Fine! Mom!" the following option is available; it is given by DeepL translator but it it is rarely used.
(Très) bien ! Maman !
For instance, when a mother is asking her son to perform a little task he can answer that way, but more often he'll say omething else: "Mom" is not used much in answering questions or demands;
- D'accord! (je le fais!)
- Oui! (je le fais!)
- Oui! (je vais le faire!)
- (as well) Ça va, je le fais!
II For "Okay! I admit it!" there are several choices that I can think of.
Bon! oui! je l'admets! That is used after some insistence from the interlocutor for you to admit something that you've somewhat grudgingly denied or that you overlooked admitting for instance; it can be used in other such similar contexts with attitudes showing various intensities of irritation, sometimes because it means giving up on a given stance.
Instead of using the two words just one can be used; this is also idiomatic, but usually the speaker doesn't show to his interlocutor feelings as intense as when he uses the two together. This is more likely the form that'll be used when there are no hard feelings. Instead of using "bon" you can use "ben" but that is quite familiar.
Eh bien, je l'admet! This is a possibility that is used most often when the person speaks with a rather neutral atitude. Nevertheless, sometimes people will use this form vehemently, when they are in a real bind and think they have no solution, being so exasperated that, seeming to want to free themselves of an oppression, they drop their opposition as their resistance simply collapses. In this case of extreme behaviour "okay" will not do, I think.
There should be not confusion with the variant used when the speaker is angry because he did admit something and that the interlocutor is not taking it into account: "Eh bien? Je l'admet!"; the translation can't be "okay" then but rather "well" (Well? I admit it!).
Eh bien, oui! je l'admet! variant of the preceding
Bien! Je l'admet! variant of the preceding
D'accord! Je l'admet! This possibility is used in plain matter of fact circumstances.