Shared Residency

Please can anyone help me with advice. My son and his partner separated earlier this year. They were not married They have a daughter now 2 1/2 who we have a wonderful relationship with.
They have a shared home. Bought with a deposit from my husband and me, and a mortgage entirely based on my son's income as the partner had very little income. My sons partner put his belongings in his car one day and told him not to come home when he was working his normal long hours to pay their mortgage.
They have had mediation which resulted in an agreement for him to have access 1 1/2 days per fortnight - basically from Friday evening to Sunday lunchtime.
Christmas is due to fall on one of Daddie's weekends but the mother has said he cannot have her for these days - she points out the mediation agreement (which they have in writing) is not legally binding. The contact takes place at our home as he has had to move back in with us - as while he continues to pay half of the mortgage and maintenance he can neither afford to rent anywhere else or get a new mortgage - he is still named on the mortgage. The partner has tried to take the mortgage on in her own name but cannot due to lack of income.
She seems to think she can get a 'Mescher' (?) order to enable her to stay in the home until our grand daughter is 18. This would effectively prevent our son providing himself with a home of his own for this length of time. (until we die and he gets half or ours!)
He is considering applying for Shared Residency to firm up his legal position - but we don't really know how this works and if fathers actually get given reasonable consideration in this.
I have tried to keep this to the legal side of my question and ignore the emotional turmoil we are all going through. If anyone can give me any advice as to how best to help our son I would be extremely grateful.
He is considering applying for the shared residency himself without a solicitor - is this realistic or would this work against him?