leaning chestnut

[Andyd1606]

Hi everyone I went to look at a small conifer removal for a customer today. The conifer is dead and is in the way of a fence that they are looking to erect. The issue I have is the rather messy chestnut that sits alongside the conifer. It is a multi stem chestnut and one of the stems is leaning on the conifer tree. I didn't want to simply remove the conifer leaving the chestnut stem under stress and leaning towards the house with the chance it would fail. The stem looks like it has grown with a kink in but this appears to have have strength in the wood. What are people's thoughts on this I have attached a few pics apologies for the quality the sun was in the wrong position. My thought on the job is to remove the conifer and take some weight from the chestnut what do people thing

Thanks