I still love my former mother-in-law. Can I keep visiting her after the divorce?

Yes; keeping ties with a good former in-law is a noble trait, all the more since she is your children's grandmother. For a former wife, the former father-in-law also remains a mahram for ever, so visiting that family raises no aurat issue with him. But your ex-husband has become a non-mahram stranger (ajnabi) to you after the iddah, so arrange visits when he is not there or when many family members are around. Let them know your intention politely so there is no misunderstanding. If the visits hurt your ex-husband or his new wife, consider other ways such as phone calls or meeting outside. Read also in-laws.