score:2
They will not refuse a visa because of this. If there is no other reason to refuse the visa, the worse I can see happening is that you would get a single-entry visa for Spain valid until the 10th of October. It would make the second part of the trip difficult to organise but you could still at least do the first part and would not have a refusal on your record.
At the end of the day, the decision will depend on some things you haven't mentioned and a refusal is always a possibility but the elements you did list (status in the UK, finances, previous travels) seem to make you a low-risk applicant. So if there is nothing unusual about the rest of your application, you are very likely to get what you need. Some people in your situation even get a one-year multiple-entry visa without asking for it.
Finally, the Schengen regulations make allowance for two-entry visas, originally intended for people who want to go to the UK in the middle of a trip to the Schengen area. That's not exactly your situation but the Spanish consulate could also use that if they are nervous about issuing a multiple-entry visa.