Please, I would like to know if the Employment details and bank statement is really necessary to add?
It is not. You already have more information than you need. In fact, if your Italian residence card says "residence card of a family member of a union citizen" then you don't even need an EEA family permit.
Do I still need to provide evidence of relationship dated back to 2012 when we started living together?
This should not be necessary.
Although, My husband was living there before I joined him, my name is neither in the utility bills nor the tenancy agreement contracts.
That should not be a problem.
If I were you, I would focus on the legal requirements:
- Your husband's nationality
- Your marriage
Some people have had a good deal of trouble with the second item, being refused for a "marriage of convenience." Since you have children and have lived together for a number of years, any refusal on these grounds would be highly improper. I would therefore include copies of the children's birth certificates and some basic evidence of your living together.
I am concerned about this item in your list:
Marriage Certificate (Modello B, copy of the Nigerian)
We recently had a question here from someone who was married in Albania and was refused after presenting the Italian document certifying their marriage. If you were married in Nigeria, then you should present a marriage certificate issued by the appropriate authority in Nigeria.
Other documents in your list could perhaps be omitted.
- Italian Permanent Residency permit (copy): This proves your legal presence in Italy, but I would include it only if it is necessary to prove that.
- Your children's ID cards are definitely not necessary, but if they show you and your husband as their parents then you could perhaps use these instead of birth certificates, but birth certificates would be preferable.
- Certificate of Residency from my commune (in Italian): this could be useful as proof of address, but the tenancy agreement might be more effective since it also shows that you live there with your husband.
- Spouse's work contract, payslips, bank statement: this is probably superfluous as there is no financial requirement for an EEA family permit.
- Your residence permit in Italy may not be necessary, but if it shows your address, include it.
- Few marriage photos and recent family photos (about 10): There should be no reason to include these, but some UK visa officers write incorrect refusal letters that assume this sort of thing should be presented. In fact, if they decide to look into whether your marriage is one of convenience, they are supposed to notify you of that and ask for additional evidence. You can include the pictures in an attempt to forestall that, but on the other hand, the officer might see something in the pictures that increases the suspicion of a marriage of convenience. It's hard to say which is more likely.