However, in this type of sentence, the example “B” would be correct because you are making a point that there are types of people, and you happen to be a specific type.

You could have just said “I love my kids” or ” I want to be with my boyfirend all the time”, but your sentences have a larger point than that, so it’s ok to mix the first person and third person.

Go with B.

It should actually be “I am a mom who loves my kids”. The easy way to work it out is to shorten – I …love my kids not I ..love her kids.

Second example would then be I …want to be with my boyfriend not I ..want to be with her boyfriend. Easy!

So “I” would normally go with ”my”.