You should definitely complain and ask to see another advisor. This is so opposite to the help I got. Granted I already had a job offer, but the lady i saw talked me through my options, worked out if i'd be better off and by how much, helped me fill in the forms, reminded me to contact the council re council tax, pointed me at a special grant to help me buy work clothes, shoes and get my hair cut and other things so i could take the job, asked me about child care options (which i didn't need then as i didn't have to work school hols). She was a single mum herself and had gone back to work after a long absense too she told me. And then they even gave me petrol money to cover my journey to the job centre and back! And that was just for a job in a local play group.
I did that job for about a year and then decided to go back to what i had done before having a child, as my son was now settled in school. I wrote to quite a few companies and got no responses. Then I found a job on the internet via a local newspaper website, phoned, was asked to come for an interview the next day, took my CV along even though I wasn't asked to, gave it to the interviewer who looked through it, asked me some questions, he asked why i was looking for this job etc and i told him my situation (single parent, one child, why i was looking for a job and what i wanted from it). I was honest about my situation. I was the first person he saw, he basically said he thought i was right for the job based on my CV and having spoken to me, but he had another more specialised job he thought would suit me better which they would train me up for and would give me better long term prospects. He did say he had to see the rest of the people on his list before he could make me a firm offer, and he rang me back later that day. I've been working there over 2 years now. Part time, flexible hours to suit me, as long as i get my work done they don't mind when i come in.
There are plenty of jobs out there. I was very lucky to find this I know but there are more out there like this i'm sure. My boss was very understanding, partly due to the fact that he brought up his two daughters on his own while working, and because i was honest with him and told him my situation up front it worked in my favour. Lots of other people in my office work part time flexible hours, some with children, some without.
The right job for you is out there somewhere. You just have to find it. Take a chance and don't listen to that advisor. Maybe you could have his job, you'd be better at it i should think!
Try cold calling your local travel agents, go in and introduce yourself to the manager. It's reckoned that 1 in 10 cold calls for a job will find you a place which has a job opening. Take your CV and leave it with them in case they get an opening even if they don't have one now. My sister got a job in a clothes shop by cold calling when she was a student.
If they have an application form fill it in and attach your CV to it as well.
Definitely don't listen to that advisor. Phone and speak to someone else and say this is what you were told and you're not happy with it, and is there someone there who can actually help you.