Land Law Problem question on co-ownership

Ellie and Paul married in 2006 and had two children, Kate and Maisy, who were born in 2013. They purchased the matrimonial home, 22 St Pauls Road, Kingston in 2006. They also purchased 44 Surbiton Road, Sutton in the same year, which is rented to tenants. The legal title was conveyed to them as joint tenants. They sold their original matrimonial home for £400,000 in 2014, and purchased Ruskin View, Hampstead for £500,000. The legal estate in the property was conveyed to them as joint tenants. The relationship broke down in 2016 and Paul left the home and went to live initially with his brother in New York, and thereafter purchased his own apartment and did not return to the UK.
In 2017, Ellie and Paul divorced however no agreement or court order was made in relation to the children, financial matters or the home. Ellie and Paul agreed that the children would stay in the UK to be educated and would stay with Paul in all the school holidays.
Ellie has paid all the bills in relation to the home since Paul moved to New York and paid for an extension to the property which was completed in 2018. The extension was to enable Ellie to work from home. She has also paid for the continuing maintenance on the rental property.
In February 2019, Ellie was diagnosed with cancer and decided to make a will, appointing her sister Antonia, as guardian for the children in the event she died. She sent a letter to Paul, stating that she had made a will and that she had appointed her sister as guardian, and that she had gifted Ruskin View to her in order to provide a stable home for the children. She explained that by reason of their separation and her illness that she wished to sever the joint tenancy in relation to both the matrimonial home and 44 Surbiton Road. The letter never reached Paul, because he had moved from the address to which the letter was sent (he had not advised Ellie of the change of address) and unbeknown to Ellie, Paul died in a car accident on the 26th January 2019. The letter was finally delivered to Paul’s new address after his death and was opened by his second wife.
1. Advise Antonia as to the legal interests in relation to both the matrimonial home and the rental property.
2. Would your advice be different if the beneficial interests in the properties were held by Ellie and Paul as tenants in common?