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My family background is as follows.

I'm holding the EEA FM residence permit and my spouse is an EU national who holds PR.
My only brother is a British Citizen married with two children.
Finally my mom is a widow and Non-EU citizen who lives by herself.

During the last few years, she's been to UK under family visit visa and stayed with me and my brother. [separate properties] She's financially dependent on us, and me and my better half sent money in last few years. We came to conclusion, that she cannot keep up with all these long distance travels and we'd like to take care of her. We both would like to apply for EEA FM resident permit for her. She's now staying with us and we're planning to apply for the visa when she's here.

However my questions are below.
1. Her current visa [family visit] and EEA FM as dependent adult are bi-polar in nature. For family visit, we need to show financial independence while for the latter other way around. Is there any point in applying for EEA FM while in a family visit visa?

2. When my mom applies for Family visit both my bro and myself provide sponsorship letters, however my mom put my brother's address as her primary address in the application. Will it affect when they process the application? Is HO cross-check every single detail in between the applications?

1) Correct.
Be aware you are unlikely to be granted any future visit visa if FM RC is refused; eg if dependency on sponsor for essential daily needs is not proven.
This is because you will have declared your hand regarding mom's intention to settle despite (presumably) proving her intent to return home in order to be granted current visit visa.

2) British brother cannot be a sponsor in EU context.
Yes, mom will have a single immigration history that is likely to be crosschecked if not analysed.

Thanks noajthan.
We understand the risk of rejection and collateral damage it can done to my mom's future travel plans to UK. It's that, we cannot see any other path for her to settle in UK with us.
However we counseled an immigration solicitor and he indicated a success rate of 70%, if we apply EEA FM RC with Article 8 HR supplement. [rejection --> appeal] Anyway we're not very convinced with all these numbers.

If anyone who got previous experience or expertise, please let me know our options here. Thanks everyone.

My understanding is HR does not figure in EU related applications (in UK) any more.

Many members have reported rejections of parental RC applications in past year; search in forum.

Safest approach would be for mom to apply for FP from home country.

Thanks again for your prompt reply.
1. Can you please explain to me, what's the advantage of applying from UK and home country assuming its the same application form?
2. She got Family Visit visa for another 4 years, therefore regardless of the applying location, we'll face the same counter argument of financial dependency, won't we?