UK Immigration Law
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You do not automatically become eligible for a British passport because your child has one.
Were you to divorce your spouses visa would be curtailed and you would have to apply for discretionary leave to remain to the Home Office citing Article 8 (Right to Private & Family Life) of Europeans Convention on Human Rights.
If you stay married then after 5 years you should apply for indefinite leave to remain. Once you have received this you should wait a further year and then apply for naturalisation. Once you have been naturalised you will be eligible to apply for a British passport.
Continue on your Visa, renewing if necessary until you reach 5 years of marriage then follow the above.
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