If in my Will I intend to leave my estate to my partner, once he dies would my estate go to his family or whoever he chooses to in his Will?

You can easily have it go to your family if he predeceases, or dies before, you: e.g. "My entire estate shall go to John Doe unless he shall predecease me, in which case, it shall go to...."
Once someone inherits money, however, it is up to them, not you, what happens to it after they die subsequent to you. The only way to control what happens to your estate after your death is to not give it directly to your partner, but to set up a trust (with a separate trustee) for his benefit: the estate will go to the trust, and the trustee will then manage and distribute it in accordance with your instructions, which can include turning over any unused portion to someone else (e.g. your family) when the beneficiary dies.
For a very simple example: say that your estate (total value of all assets, including real estate) would be $500k; we will ignore interest (e.g. if it is invested) for simplicity's sake. Say you believe that your partner would be helped by $25k per year in additional money. You could have your will create a "testamentary trust" for his benefit where the trustee will distribute him $25k on the 1st of each year (or a bit of over $2km/month, if you'd rather do it that way) for the next 20 years. If your partner dies before the entire estate is used up, your trustee would be directed to distribute the remainder to certain named family members of yours. 
You can set up a trust almost any way you want--equal payments over time; large payments every several years; paying certain bills and expenses for the beneficiary, rather than giving him money directly; etc. But the point is, to keep control over the money, it must be in a trust, since once it is given to a person, it is his to decide what to do with. 
If you wish to explore setting up a trust, consult with a trusts and estates attorney.